## Cylinder Volume Calculator

How to calculate volume of a cylinder, volume of a hollow cylinder, volume of an oblique cylinder.

Our cylinder volume calculator enables calculating the volume of that solid. Whether you want to figure out how much water fits in a can, coffee in your favorite mug, or even the volume of a drinking straw – you're in the right place. The other option is calculating the volume of a cylindrical shell (hollow cylinder).

Let's start from the beginning – what is a cylinder? It's a solid bounded by a cylindrical surface and two parallel planes. We can imagine it as a solid physical tin having lids on top and bottom. To calculate its volume, we need to know two parameters – the radius (or diameter) and height:

cylinder volume = π × cylinder radius² × cylinder height

The cylinder volume calculator helps in finding the volume of right, hollow and oblique cylinders:

The hollow cylinder, also called the cylindrical shell, is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis.

It's easier to understand that definition by imagining, e.g., a drinking straw or a pipe – the hollow cylinder is this plastic, metal, or other material. The formula behind the volume of a hollow cylinder is:

cylinder_volume = π × (R² - r²) × cylinder_height

where R – external radius, and r – internal radius

Similarly, we can calculate the cylinder volume using the external diameter, D , and internal diameter, d , of a hollow cylinder with this formula:

cylinder_volume = π × [(D² - d²)/4] × cylinder_height

To calculate the volume of a cylindrical shell, let's take some real-life examples, maybe... a roll of toilet paper, because why not? 😀

Enter the external diameter of the cylinder . The standard is equal to approximately 11 cm.

Determine the internal cylinder diameter . It's the internal diameter of the cardboard part, around 4 cm.

Find out what's the height of the cylinder ; for us, it's 9 cm.

Tadaaam! The volume of a hollow cylinder is equal to 742.2 cm³.

Remember that the result is the volume of the paper and the cardboard. If you want to calculate how much plasticine you can put inside the cardboard roll, use the standard formula for the volume of a cylinder – the calculator will calculate it in the blink of an eye!

The oblique cylinder is the one that 'leans over' – the sides are not perpendicular to the bases in contrast to a standard 'right cylinder'. How to calculate the volume of an oblique cylinder? The formula is the same as for the straight one. Just remember that the height must be perpendicular to the bases.

Now that you know how to calculate a volume of a cylinder, maybe you want to determine the volumes of other 3D solids? Use this general volume calculator !

If you are curious about how many teaspoons or cups fit into your container, use our volume converter .

To calculate the volume of soil needed for flower pots of different shapes – also for the cylindrical one – use the potting soil calculator .

## Where can you find cylinders in nature?

Cylinders are all around us , and we are not just talking about Pringles’ cans. Although things in nature are rarely perfect cylinders, some examples are tree trunks & plant stems, some bones (and therefore bodies), and the flagella of microscopic organisms. These make up a large amount of the natural objects on Earth!

## How do you draw a cylinder?

To draw a cylinder, follow these steps:

Draw a slightly flattened circle. The more flattened it is, the closer you are to looking at the cylinder side on .

Draw two equal, parallel lines from the far sides of your circle going down.

Link the ends of the two lines with a semi-circular line that looks the same as the bottom half of your top circle.

Add shadow and shading as appropriate.

## How do you calculate the weight of a cylinder?

To calculate the weight of a cylinder:

Square the radius of the cylinder .

Multiply the square of radius by pi and the cylinder’s height .

Multiply the volume by the density of the cylinder. The result is the cylinder’s weight.

## How do you calculate the surface area to volume ratio of a cylinder?

Find the volume of the cylinder using the formula πr²h .

Find the surface area of the cylinder using the formula 2πrh + 2πr² .

Make a ratio out of the two formulas, i.e., πr²h : 2πrh + 2πr² .

Alternatively, simplify it to rh : 2(h+r) .

Divide both sides by one of the sides to get the ratio in its simplest form.

## How do you find the height of a cylinder?

If you have the volume and radius of the cylinder:

- Make sure the volume and radius are in the same units (e.g., cm³ and cm).

Square the radius.

- Divide the volume by the radius squared and pi to get the height in the same units as the radius.

If you have the surface area and radius (r):

- Make sure the surface and radius are in the same units .
- Subtract 2πr² from the surface area.
- Divide the result of step 2 by 2πr.
- The result is the height of the cylinder.

## How do I find the radius of a cylinder?

If you have the volume and height of the cylinder:

- Make sure the volume and height are in the same units (e.g., cm³ and cm).
- Divide the volume by pi and the height.
- Square root the result.

If you have the surface area and height (h):

- Substitute the height, h, and surface area into the equation, surface area = 2πrh + 2πr².
- Divide both sides by 2π.
- Subtract surface area/2π from both sides.
- Solve the resulting quadratic equation.
- The positive root is the radius.

## How do you find the volume of an oval cylinder?

To find the volume of an oval cylinder:

Multiply the smallest radius of the oval (minor axis) by its largest radius (major axis).

Multiply this new number by pi .

Divide the result of step 2 by 4. The result is the area of the oval.

Multiply the area of the oval by the height of the cylinder.

The result is the volume of an oval cylinder.

## How do you find the volume of a slanted cylinder?

To calculator the volume of a slanted cylinder:

Find the radius, side length, and slant angle of the cylinder.

Multiply the result by pi.

Take the sin of the angle .

Multiply the sin by the side length.

Multiply the result from steps 3 and 5 together.

The result is the slanted volume.

## How do you calculate the swept volume of a cylinder?

To compute the swept volume of a cylinder:

Divide the bore diameter by 2 to get the bore radius .

Square the bore radius.

Multiply the square radius by pi.

Multiply the result of step 3 by the length of the stroke . Make sure the units for bore and stroke length are the same.

The result is the swept volume of one cylinder.

## Area of triangle with coordinates

Circumference, multiplying exponents.

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## Volume of a Cylinder

The worksheets below can be used to help teach students how to calculate the volumes of cylinders. The basic level worksheets do not include decimal measurements. The advanced level includes decimals and/or fractional measurements.

## Level: Basic

Logged in members can use the Super Teacher Worksheets filing cabinet to save their favorite worksheets.

Quickly access your most used files AND your custom generated worksheets!

Please login to your account or become a member and join our community today to utilize this helpful feature.

## Level : Advanced

From this page you can download a collection of worksheets on calculating the volumes of rectangular prisms.

## Sample Worksheet Images

PDF with answer key:

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## Volume of Cylinders

A cylinder is a solid with two congruent circles joined by a curved surface.

In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height. Since the base is a circle and the area of a circle is πr 2 then the volume of the cylinder is πr 2 × h.

Volume of cylinder = πr 2 h

Surface Area of cylinder = 2πr 2 + 2πrh

Calculate the volume of a cylinder where:

a) the area of the base is 30 cm 2 and the height is 6 cm. b) the radius of the base is 14 cm and the height is 10 cm.

Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe.

Volume of hollow cylinder: = πR 2 h – πr 2 h = πh (R 2 – r 2 )

The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.

Solution: The cross section of the pipe is a ring: Area of ring = [ π (2.4) 2 – π (2) 2 ]= 1.76 π cm 2

These videos show how to solve word problems about cylinders.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

## Volume of a Cylinder Calculator

Use this cylinder volume calculator to easily calculate the volume of a cylinder from its base radius and height in any metric: mm, cm, meters, km, inches, feet, yards, miles...

## Calculation results

Related calculators.

- Volume of a cylinder formula
- How to calculate the volume of a cylinder?
- Example: find the volume of a cylinder
- Practical applications

## Volume of a cylinder formula

The formula for the volume of a cylinder is height x π x (diameter / 2) 2 , where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius 2 . Visual in the figure below:

First, measure the diameter of the base (usually easier than measuring the radius), then measure the height of the cylinder. To do the calculation properly, you must have the two measurements in the same length units. The result from our volume of a cylinder calculator is always in cubic units, based on the input unit: in 3 , ft 3 , yd 3 , cm 3 , m 3 , km 3 , and so on.

## How to calculate the volume of a cylinder?

One can think of a cylinder as a series of circles stacked one upon another. The height of the cylinder gives us the depth of stacking, while the area of the base gives us the area of each circular slice. Multiplying the area of the slice by the depth of the stack is an easy way to conceptualize the way for calculating the volume of a cylinder. Since in practical situations it is easier to measure the diameter (of a tube, a round steel bar, a cable, etc.) than it is to measure the radius, and on most technical schemes it is the diameter which is given, our cylinder volume calculator accepts the diameter as an input. If you have the radius instead, just multiply it by two.

Using the formula and doing the calculations by hand can be difficult due to the value of the π constant: ~3.14159, which can be hard to work with, so a volume of a cylinder calculator significantly simplifies the task.

## Example: find the volume of a cylinder

Applying the volume formulas is easy provided the cylinder height is known and one of the following is also given: the radius, the diameter, or the area of the base. For example, if the height and area are given to be 5 feet and 20 square feet, the volume is just a multiplication of the two: 5 x 20 = 100 cubic feet.

If the radius is given, using the second equation above can give us the cylinder volume with a few additional steps. For example, the height is 10 inches and the radius is 2 inches. First, we find the area by 3.14159 x 2 2 = 3.14159 x 4 = 12.574, then multiply that by 10 to get 125.74 cubic inches of volume. Using a higher level of precision for π results in more accurate results, e.g. our calculator computes the volume of this cylinder as 125.6637 cu in.

## Practical applications

The cylinder is one of the most widely used body shapes in engineering and architecture: from tunnels, covered walkways to tubes, cables, round bars, the cylinders and pistons in your car's engine - cylinders are everywhere. Calculating cylinder volume is useful when you want to know its displacement, or how much liquid or gas you need to fill it, e.g. how much water you need to fill your jacuzzi. Cylindrical aquariums are also fairly common, so are cylindrical artificial lakes, fountains, gas containers / tanks, etc.

## Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Volume of a Cylinder Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/volume-of-cylinder-calculator.php URL [Accessed Date: 25 Feb, 2024].

## Geometry calculators

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## How to Calculate the Volume of a Cylinder

Last Updated: January 11, 2024 References

This article was co-authored by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 3,940,012 times.

A cylinder is a simple geometric shape with two equally-sized and parallel circular bases. Calculating the volume of a cylinder is simple once you know the formula. [1] X Research source

## Help Finding the Volume of a Cylinder

## Calculating the Volume of a Cylinder

- If you know the diameter of the circle, just divide it by 2. [3] X Research source
- If you know the circumference, then you can divide it by 2π to get the radius. [4] X Research source

- A = π x 1 2
- Since π is normally rounded to 3.14, you can say that the area of the circular base is 3.14 in. 2

- Always state your final answer in cubic units because volume is the measure of a three-dimensional space. [10] X Research source

## Community Q&A

- Remember the diameter is the biggest chord in a circle or in a circumference, i.e. the biggest measurement you can get between two points in a circumference or in the circle within. The edge of the circle should meet the zero mark in your ruler/flex tape, and the biggest measurement you obtain without losing contact with your zero mark will be the diameter. [11] X Research source Thanks Helpful 1 Not Helpful 0
- Make up a few problems to practice so you know that you will get it right when you try it for real. Thanks Helpful 11 Not Helpful 3
- The volume of a cylinder is given by the formula V = πr 2 h, and π is about the equivalent of 22/7 or 3.14. Thanks Helpful 11 Not Helpful 10

## Tips from our Readers

- To approximate the area of a circle, square its diameter, then multiply that by .7854. It's not precise, but it helps in a pinch.

## You Might Also Like

- ↑ https://www.mathsisfun.com/definitions/cylinder.html
- ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
- ↑ https://www.mathsisfun.com/definitions/radius.html
- ↑ https://www.mathsisfun.com/definitions/pi.html
- ↑ https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-circumference-circle/v/area-of-a-circle
- ↑ https://www.mathopenref.com/cylindervolume.html
- ↑ https://www.mathsisfun.com/definitions/volume.html
- ↑ https://www.cut-the-knot.org/pythagoras/Munching/DiameterChord.shtml

## About This Article

1. Measure the circular base to get the diameter. 2. Divide the diameter by 2 to get the radius. 3. Calculate the area with the formula: A = πr^2, where r is the radius. 4. Measure the height of the cylinder. 5. Multiply the area by the height to get the Volume. Did this summary help you? Yes No

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## Volume Worksheets

This humongous collection of printable volume worksheets is sure to walk middle and high school students step-by-step through a variety of exercises beginning with counting cubes, moving on to finding the volume of solid shapes such as cubes, cones, rectangular and triangular prisms and pyramids, cylinders, spheres and hemispheres, L-blocks, and mixed shapes. Brimming with learning and backed by application the PDFs offer varied levels of difficulty.

## List of Volume Worksheets

Counting Cubes

- Volume of Cubes
- Volume of Rectangular Prisms
- Volume of Triangular Prisms

Volume of Mixed Prisms

- Volume of Cones
- Volume of Cylinders

Volume of Spheres and Hemispheres

- Volume of Rectangular Pyramids
- Volume of Triangular Pyramids

Volume of Mixed Pyramids

Volume of Mixed Shapes

Volume of Composite Shapes

## Explore the Volume Worksheets in Detail

Work on the skill of finding volume with this batch of counting cubes worksheets. Count unit cubes to determine the volume of rectangular prisms and solid blocks, draw prisms on isometric dot paper and much more.

Volume of a Cube

Augment practice with this unit of pdf worksheets on finding the volume of a cube comprising problems presented as shapes and in the word format with side length measures involving integers, decimals and fractions.

Volume of a Rectangular Prism

This batch of volume worksheets provides a great way to learn and perfect skills in finding the volume of rectangular prisms with dimensions expressed in varied forms, find the volume of L-blocks, missing measure and more.

Volume of a Triangular Prism

Encourage students to work out the entire collection of printable worksheets on computing the volume of triangular prism using the area of the cross-section or the base and leg measures and practice unit conversions too.

Navigate through this collection of volume of mixed prism worksheets featuring triangular, rectangular, trapezoidal and polygonal prisms. Bolster practice with easy and moderate levels classified based on the number range used.

Volume of a Cone

Motivate learners to use the volume of a cone formula efficiently in the easy level, find the radius in the moderate level and convert units in the difficult level, solve for volume using slant height, and find the volume of a conical frustum too.

Volume of a Cylinder

Access our volume of a cylinder worksheets to practice finding the radius from diameter, finding the volume of cylinders with parameters in integers and decimals, find the missing parameters, solve word problems and more!

Take the hassle out of finding the volume of spheres and hemispheres with this compilation of pdf worksheets. Gain immense practice with a wide range of exercises involving integers and decimals.

Volume of a Rectangular Pyramid

This exercise is bound to help learners work on the skill of finding the volume of rectangular pyramids with dimensions expressed as integers, decimals and fractions in easy and moderate levels.

Volume of a Triangular Pyramid

Help children further their practice with this bundle of pdf worksheets on determining the volume of triangular pyramids using the measures of the base area or height and base. The problems are offered as 3D shapes and in word format in varied levels of difficulty.

Gain ample practice in finding the volume of pyramids with triangular, rectangular and polygonal base faces presented in two levels of difficulty. Apply relevant formulas to find the volume using the base area or the other dimensions provided.

Upscale practice with an enormous collection of printable worksheets on finding the volume of solid shapes like prisms, cylinders, cones, pyramids and revision exercises to revisit concepts with ease.

Learn to find the volume of composite shapes that are a combination of two or more solid 3D shapes. Begin with counting squares, find the volume of L -blocks, and compound shapes by adding or subtracting volumes of decomposed shapes.

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## Lesson Volume of cylinders

## Volume Calculator

The following is a list of volume calculators for several common shapes. Please fill in the corresponding fields and click the "Calculate" button.

## Sphere Volume Calculator

## Cone Volume Calculator

## Cube Volume Calculator

## Cylinder Volume Calculator

## Rectangular Tank Volume Calculator

## Capsule Volume Calculator

## Spherical Cap Volume Calculator

Please provide any two values below to calculate.

## Conical Frustum Volume Calculator

## Ellipsoid Volume Calculator

## Square Pyramid Volume Calculator

## Tube Volume Calculator

Related Surface Area Calculator | Area Calculator

Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter, or m 3 . By convention, the volume of a container is typically its capacity, and how much fluid it is able to hold, rather than the amount of space that the actual container displaces. Volumes of many shapes can be calculated by using well-defined formulas. In some cases, more complicated shapes can be broken down into simpler aggregate shapes, and the sum of their volumes is used to determine total volume. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary. Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite element method. Alternatively, if the density of a substance is known, and is uniform, the volume can be calculated using its weight. This calculator computes volumes for some of the most common simple shapes.

A sphere is the three-dimensional counterpart of a two-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the set of points that are equidistant from a given point at its center, where the distance between the center and any point on the sphere is the radius r . Likely the most commonly known spherical object is a perfectly round ball. Within mathematics, there is a distinction between a ball and a sphere, where a ball comprises the space bounded by a sphere. Regardless of this distinction, a ball and a sphere share the same radius, center, and diameter, and the calculation of their volumes is the same. As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter, d . The equation for calculating the volume of a sphere is provided below:

EX: Claire wants to fill a perfectly spherical water balloon with radius 0.15 ft with vinegar to use in the water balloon fight against her arch-nemesis Hilda this coming weekend. The volume of vinegar necessary can be calculated using the equation provided below:

volume = 4/3 × π × 0.15 3 = 0.141 ft 3

A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a set of line segments connected to a common center point, except that the center point is not included in the plane that contains the circle (or some other base). Only the case of a finite right circular cone is considered on this page. Cones comprised of half-lines, non-circular bases, etc. that extend infinitely will not be addressed. The equation for calculating the volume of a cone is as follows:

where r is the radius and h is the height of the cone

EX: Bea is determined to walk out of the ice cream store with her hard-earned $5 well spent. While she has a preference for regular sugar cones, the waffle cones are indisputably larger. She determines that she has a 15% preference for regular sugar cones over waffle cones and needs to determine whether the potential volume of the waffle cone is ≥ 15% more than that of the sugar cone. The volume of the waffle cone with a circular base with radius 1.5 in and height 5 in can be computed using the equation below:

volume = 1/3 × π × 1.5 2 × 5 = 11.781 in 3

Bea also calculates the volume of the sugar cone and finds that the difference is < 15%, and decides to purchase a sugar cone. Now all she has to do is use her angelic, childlike appeal to manipulate the staff into emptying the containers of ice cream into her cone.

A cube is the three-dimensional analog of a square, and is an object bounded by six square faces, three of which meet at each of its vertices, and all of which are perpendicular to their respective adjacent faces. The cube is a special case of many classifications of shapes in geometry, including being a square parallelepiped, an equilateral cuboid, and a right rhombohedron. Below is the equation for calculating the volume of a cube:

volume = a 3 where a is the edge length of the cube

EX: Bob, who was born in Wyoming (and has never left the state), recently visited his ancestral homeland of Nebraska. Overwhelmed by the magnificence of Nebraska and the environment unlike any other he had previously experienced, Bob knew that he had to bring some of Nebraska home with him. Bob has a cubic suitcase with edge lengths of 2 feet, and calculates the volume of soil that he can carry home with him as follows:

volume = 2 3 = 8 ft 3

A cylinder in its simplest form is defined as the surface formed by points at a fixed distance from a given straight line axis. In common use, however, "cylinder" refers to a right circular cylinder, where the bases of the cylinder are circles connected through their centers by an axis perpendicular to the planes of its bases, with given height h and radius r . The equation for calculating the volume of a cylinder is shown below:

volume = πr 2 h where r is the radius and h is the height of the tank

EX: Caelum wants to build a sandcastle in the living room of his house. Because he is a firm advocate of recycling, he has recovered three cylindrical barrels from an illegal dumping site and has cleaned the chemical waste from the barrels using dishwashing detergent and water. The barrels each have a radius of 3 ft and a height of 4 ft, and Caelum determines the volume of sand that each can hold using the equation below:

volume = π × 3 2 × 4 = 113.097 ft 3

He successfully builds a sandcastle in his house, and as an added bonus, manages to save electricity on nighttime lighting, since his sandcastle glows bright green in the dark.

## Rectangular Tank

A rectangular tank is a generalized form of a cube, where the sides can have varying lengths. It is bounded by six faces, three of which meet at its vertices, and all of which are perpendicular to their respective adjacent faces. The equation for calculating the volume of a rectangle is shown below:

volume= length × width × height

EX: Darby likes cake. She goes to the gym for 4 hours a day, every day, to compensate for her love of cake. She plans to hike the Kalalau Trail in Kauai and though extremely fit, Darby worries about her ability to complete the trail due to her lack of cake. She decides to pack only the essentials and wants to stuff her perfectly rectangular pack of length, width, and height 4 ft, 3 ft and 2 ft respectively, with cake. The exact volume of cake she can fit into her pack is calculated below:

volume = 2 × 3 × 4 = 24 ft 3

A capsule is a three-dimensional geometric shape comprised of a cylinder and two hemispherical ends, where a hemisphere is half a sphere. It follows that the volume of a capsule can be calculated by combining the volume equations for a sphere and a right circular cylinder:

where r is the radius and h is the height of the cylindrical portion

EX: Given a capsule with a radius of 1.5 ft and a height of 3 ft, determine the volume of melted milk chocolate m&m's that Joe can carry in the time capsule he wants to bury for future generations on his journey of self-discovery through the Himalayas:

volume = π × 1.5 2 × 3 + 4/3 ×π ×1.5 3 = 35.343 ft 3

## Spherical Cap

A spherical cap is a portion of a sphere that is separated from the rest of the sphere by a plane. If the plane passes through the center of the sphere, the spherical cap is referred to as a hemisphere. Other distinctions exist, including a spherical segment, where a sphere is segmented with two parallel planes and two different radii where the planes pass through the sphere. The equation for calculating the volume of a spherical cap is derived from that of a spherical segment, where the second radius is 0. In reference to the spherical cap shown in the calculator:

Given two values, the calculator provided computes the third value and the volume. The equations for converting between the height and the radii are shown below:

EX: Jack really wants to beat his friend James in a game of golf to impress Jill, and rather than practicing, he decides to sabotage James' golf ball. He cuts off a perfect spherical cap from the top of James' golf ball, and needs to calculate the volume of the material necessary to replace the spherical cap and skew the weight of James' golf ball. Given James' golf ball has a radius of 1.68 inches, and the height of the spherical cap that Jack cut off is 0.3 inches, the volume can be calculated as follows:

volume = 1/3 × π × 0.3 2 (3 × 1.68 - 0.3) = 0.447 in 3

Unfortunately for Jack, James happened to receive a new shipment of balls the day before their game, and all of Jack's efforts were in vain.

## Conical Frustum

A conical frustum is the portion of a solid that remains when a cone is cut by two parallel planes. This calculator calculates the volume for a right circular cone specifically. Typical conical frustums found in everyday life include lampshades, buckets, and some drinking glasses. The volume of a right conical frustum is calculated using the following equation:

where r and R are the radii of the bases, h is the height of the frustum

EX: Bea has successfully acquired some ice cream in a sugar cone, and has just eaten it in a way that leaves the ice cream packed within the cone, and the ice cream surface level and parallel to the plane of the cone's opening. She is about to start eating her cone and the remaining ice cream when her brother grabs her cone and bites off a section of the bottom of her cone that is perfectly parallel to the previously sole opening. Bea is now left with a right conical frustum leaking ice cream, and has to calculate the volume of ice cream she must quickly consume given a frustum height of 4 inches, with radii 1.5 inches and 0.2 inches:

volume=1/3 × π × 4(0.2 2 + 0.2 × 1.5 + 1.5 2 ) = 10.849 in 3

An ellipsoid is the three-dimensional counterpart of an ellipse, and is a surface that can be described as the deformation of a sphere through scaling of directional elements. The center of an ellipsoid is the point at which three pairwise perpendicular axes of symmetry intersect, and the line segments delimiting these axes of symmetry are called the principal axes. If all three have different lengths, the ellipsoid is commonly described as tri-axial. The equation for calculating the volume of an ellipsoid is as follows:

where a , b , and c are the lengths of the axes

EX: Xabat only likes eating meat, but his mother insists that he consumes too much, and only allows him to eat as much meat as he can fit within an ellipsoid shaped bun. As such, Xabat hollows out the bun to maximize the volume of meat that he can fit in his sandwich. Given that his bun has axis lengths of 1.5 inches, 2 inches, and 5 inches, Xabat calculates the volume of meat he can fit in each hollowed bun as follows:

volume = 4/3 × π × 1.5 × 2 × 5 = 62.832 in 3

## Square Pyramid

A pyramid in geometry is a three-dimensional solid formed by connecting a polygonal base to a point called its apex, where a polygon is a shape in a plane bounded by a finite number of straight line segments. There are many possible polygonal bases for a pyramid, but a square pyramid is a pyramid in which the base is a square. Another distinction involving pyramids involves the location of the apex. A right pyramid has an apex that is directly above the centroid of its base. Regardless of where the apex of the pyramid is, as long as its height is measured as the perpendicular distance from the plane containing the base to its apex, the volume of the pyramid can be written as:

EX: Wan is fascinated by ancient Egypt and particularly enjoys anything related to the pyramids. Being the eldest of his siblings Too, Tree and Fore, he is able to easily corral and deploy them at his will. Taking advantage of this, Wan decides to re-enact ancient Egyptian times and have his siblings act as workers building him a pyramid of mud with edge length 5 feet and height 12 feet, the volume of which can be calculated using the equation for a square pyramid:

volume = 1/3 × 5 2 × 12 = 100 ft 3

## Tube Pyramid

A tube, often also referred to as a pipe, is a hollow cylinder that is often used to transfer fluids or gas. Calculating the volume of a tube essentially involves the same formula as a cylinder ( volume=pr 2 h ), except that in this case, the diameter is used rather than the radius, and length is used rather than height. The formula, therefore, involves measuring the diameters of the inner and outer cylinder, as shown in the figure above, calculating each of their volumes, and subtracting the volume of the inner cylinder from that of the outer one. Considering the use of length and diameter mentioned above, the formula for calculating the volume of a tube is shown below:

where d 1 is the outer diameter, d 2 is the inner diameter, and l is the length of the tube

EX: Beulah is dedicated to environmental conservation. Her construction company uses only the most environmentally friendly of materials. She also prides herself on meeting customer needs. One of her customers has a vacation home built in the woods, across a creek. He wants easier access to his house, and requests that Beulah build him a road, while ensuring that the creek can flow freely so as not to disrupt his favorite fishing spot. She decides that the pesky beaver dams would be a good point to build a pipe through the creek. The volume of patented low-impact concrete required to build a pipe of outer diameter 3 feet, inner diameter 2.5 feet, and length of 10 feet, can be calculated as follows:

## Common Volume Units

- → Resources
- → 8th Grade

## Volume of Cylinders, Cones, and Spheres Lesson Plan

Get the lesson materials.

## Volume of Cylinders, Cones, and Spheres Guided Notes

Ever wondered how to teach volume calculations of cylinders, cones and spheres in an engaging way to your 8th grade students? In this lesson plan, students will learn about volume calculations and their real-life applications.

Through artistic, interactive guided notes, check for understanding, maze, doodle & color by number activities, and real-life application of paint in a can, students will gain a comprehensive understanding of volume calculations.

The lesson culminates with a real life example that explores how the volume calculation is used in measuring paint in a can.

- Type : Lesson Plans
- Grade : 8th Grade
- Standard : CCSS 8.G.C.9

## Learning Objectives

After this lesson, students will be able to:

Know the formulas for the volume of cylinders, cones, and spheres

Calculate the volume of cylinders, cones, and spheres

Apply the concept of volume to real-life situations, such as measuring the volume of paint in a can.

## Prerequisites

Before this lesson, students should be familiar with:

Basic multiplication and division skills

How to evaluate exponents (powers of 2 and 3)

Basic understanding of fractions and decimals (optional, but helpful)

Colored pencils or markers

Volume of Cylinders, Cones, & Spheres

Guided Notes

## Key Vocabulary

Cubic Units

## Introduction

As a hook, ask students why it is important to be able to calculate the volume of objects like cylinders, cones, and spheres. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the guided notes to introduce the concept of finding volume of cylinders, cones, and spheres. Walk through the key points of the topic of the guided notes to teach. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Have students walk through the “Volume Practice” section. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Have students practice finding the volume of cylinders, cones, and spheres using the Doodle Math activity. Walk around to answer student questions.

Fast finishers can dive into the maze for extra practice. You can assign it as homework for the remainder of the class.

## Real-Life Application

Bring the class back together, and introduce the concept of measuring the volume of paint in a can. Explain how understanding the volume of the can and the amount of paint inside can help determine how much paint is needed for a project, and how it can save time and money by avoiding over-purchasing paint.

Refer to the FAQs below for more ideas on how to teach this real-life application.

## Additional self-checking digital practice

If you’re looking for digital practice for volume calculations of cylinders, cones, and spheres, try the Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun and a powerful tool for differentiation.

Volume of Cylinders, Cones, and Spheres 3 Pixel Art

## Additional print practice

A fun, no-prep way to practice volume calculations of cylinders, cones, and spheres is Doodle & Color by Number — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Volume of Cylinders, Cones, & Spheres Doodle & Color by Number

## What is the formula for finding the volume of a cylinder? Open

The formula for finding the volume of a cylinder is pi times the radius squared times the height of the cylinder.

## What is the formula for finding the volume of a cone? Open

The formula for finding the volume of a cone is one-third times pi times the radius squared times the height of the cone.

## What is the formula for finding the volume of a sphere? Open

The formula for finding the volume of a sphere is four-thirds times pi times the radius cubed.

## Why is it important to know how to calculate the volume of objects like cylinders, cones, and spheres? Open

Knowing how to calculate the volume of objects like cylinders, cones, and spheres is important in many real-life situations, such as measuring the volume of paint in a can or calculating the volume of objects such as traffic cones, and even megaphones.

## What are cubic units? Open

Cubic units are units of measurement used to measure the volume of objects in three-dimensional space.

## What is an exponent? Open

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself.

## Want more ideas and freebies?

Get my free resource library with digital & print activities—plus tips over email.

## Mrs. Smith's Class

“it is not that i'm so smart. but i stay with the questions much longer.” ~ albert einstein, unit 8 – volume and surface area.

Wed. January 14 Lesson: ASSIGNMENT REVIEW DAY – In-Class Assignment TOMORROW! Homework: Unit 8 Assignment Review Questions ; Unit 8 Assignment Review (SOLUTIONS)

Tues. January 13 Lesson: Surface Area of Cylinders, Spheres, and Cones (Lesson Notes) Homework: Surface Area of Cylinders, Spheres, and Cones (Homeworkd w Solutions)

Mon. January 12 Lesson: Surface Area of Prisms & Pyramids (Lesson Notes) Homework: Surface Area of Prisms & Pyramids (HOMEWORK w Answers)

Fri. January 9 Lesson: Volume of Cylinders, Cones, & Spheres (Lesson Notes) Homework: Volume of Cylinders, Cones, & Spheres (Handout & Worksheet)

Thurs. January 8 Lesson: Culminating Activity Work Period – DUE THIS FRIDAY JAN. 9

Wed. January 7 Lesson: Volume of Prisms & Pyramids (Lesson Notes) Homework: Volume of Prisms & Pyramids (HOMEWORK)

Tues. January 6 Lesson: Imperial Conversions (Lesson Notes) Homework: Imperial System (Homework)

Mon. January 5 Lesson: Metric System (Lesson Notes) Homework: Metric Conversion Worksheet

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## Course: 8th grade > Unit 5

- Cylinder volume & surface area
- Volume of cylinders
- Volume of a sphere
- Volume of spheres
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## Volume of cylinders, spheres, and cones word problems

- Geometry: FAQ
- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
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## Volume of prisms and cylinders practice

## Volume of Cylinders & Prisms : Notes & Practice

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## What is the Volume of a Robot Art Project Activity...This is AWESOME Practice !!

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## Volume and Surface Area of Rectangular Prisms and Cylinders - Editable Foldable

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## Surface Area & Volume (UNIT 11) - Guided Notes & Practice BUNDLE

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## Volume of Prisms and Cylinders DIGITAL Scavenger Hunt Distance Learning

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## Maneuvering The Middle Llc 2016 Volume Of Cylinders

Maneuvering The Middle Llc 2016 Volume Of Cylinders - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Section volume of cylinders cones and spheres, Volumes of cones, Volume, Unit b homework helper answer key, Pythagorean theorem practice 1, 10 identifying solid figures, Scatter plots, Answer key volume of rectangular prisms.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

## 1. Section 8.3: Volume of Cylinders, Cones, and Spheres

2. 7.4 volumes of cones, 4. unit b homework helper answer key, 5. pythagorean theorem practice 1, 6. 10-identifying solid figures, 7. scatter plots, 8. answer key volume of rectangular prisms.

## COMMENTS

FAQ Our cylinder volume calculator enables calculating the volume of that solid. Whether you want to figure out how much water fits in a can, coffee in your favorite mug, or even the volume of a drinking straw - you're in the right place. The other option is calculating the volume of a cylindrical shell (hollow cylinder).

Volume of cylinders. Find the volume of the cylinder. Either enter an exact answer in terms of π or use 3.14 for π . Stuck? Review related articles/videos or use a hint. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the ...

Level : Advanced Volume of a Cylinder (Basic) The top of this page is an explanation of how to find the volume of a cylinder. Beneath that are six problems for students to solve. 7th and 8th Grades View PDF Calculate Volumes of Cylinders (Advanced) Calculate the volume of 9 different cylinders.

Solution: a) V = Area of base × height = 30 cm 2 × 6 am = 180 cm 3 b) How to find the volume of a cylinder? Examples: 1. Find the volume of cylinder with radius of 5.5 feet and a height of 11.4 feet. 2. Find the volume of cylinder with diameter of 12 inches and a height of 29 inches. Show Step-by-step Solutions

Apply the volume of a cylinder formula V = πr 2 h, substitute the value of the radius and height in the formula and compute the volume of each cylinder. Download the set Volume of a Cylinder | Decimals - Difficult Augment your practice in finding the volume of cylinders involving unit conversions.

The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2. Visual in the figure below: First, measure the diameter of the base (usually easier than measuring the radius), then measure the height of the cylinder.

Our Surface Area & Volume Worksheets are free to download, easy to use, and very flexible. These Surface Area & Volume Worksheets are a great resource for children in 5th, 6th Grade, 7th Grade, and 8th Grade. Click here for a Detailed Description of all the Geometry Worksheets. Quick Link for All Geometry Worksheets

A = π x 1. A = π. Since π is normally rounded to 3.14, you can say that the area of the circular base is 3.14 in. 2. 3. Find the height of the cylinder. [7] If you know the height already, move on. If not, use a ruler to measure it. The height is the distance between the edges of the two bases.

CBSE Math Volume of Cylinders Summary: The measure of the space occupied by a solid is called its volume. The units of surface area are square cm (i.e., cm 2 ), square meter (i.e., m 2 ), etc. Volume of cylinder, V cylinder = π r 2 h Volume of material used for hollow cylinder = π h ( R 2 − r 2) Select from the frequently asked questions below.

Math Grade 8 Volume of Cylinders Summary: Volume is the amount of space inside a 3D solid measured in cubic units. A prism is a solid made of flat sides with two parallel and congruent bases. Its volume is found by multiplying the area of the base by the height, or V = B ⋅ h. A cylinder is a solid with two parallel and congruent circular bases.

1 ACTIVITY: Finding a Formula Experimentally Work with a partner. a. Find the area of the face of a coin. b. Find the volume of a stack of a dozen coins. c. Write a formula for the volume of a cylinder. height â h 2 COMMON CORE Geometry In this lesson, you will fi nd the volumes of cylinders. fi nd the heights of cylinders given the volumes.

Access our volume of a cylinder worksheets to practice finding the radius from diameter, finding the volume of cylinders with parameters in integers and decimals, find the missing parameters, solve word problems and more! Volume of Spheres and Hemispheres

1. Describe what volume is. Compare it to finding perimeter or area. To help us better understand how important it is to know how to find the volume of a three-dimensional object do the following activity. 2. Choose two different sizes of cylindrical cans to use for this activity. Measure the diameter and the height of each can in centimeters.

Find the volume of a cylinder if its radius is of 5 cm and the height is of 4 cm. Solution The volume of the cylinder is = = * * = 3.14159*25*4 = 3.14159*100 = 314.159 (approximately). Answer. The volume of the cylinder is 314.159 (approximately). Example 2 Two cylinders are joined in a way that the base of one cylinder is overposed on the base ...

Volume = Find the exact volume of each cylinder. 1) 6 m Volume = 396π m 4) 6 m Volume = 45π m 7) 11 cm Volume =

The volume of the waffle cone with a circular base with radius 1.5 in and height 5 in can be computed using the equation below: volume = 1/3 × π × 1.5 2 × 5 = 11.781 in 3. Bea also calculates the volume of the sugar cone and finds that the difference is < 15%, and decides to purchase a sugar cone.

Use the guided notes to introduce the concept of finding volume of cylinders, cones, and spheres. Walk through the key points of the topic of the guided notes to teach. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions. Have students walk through the "Volume Practice" section.

Lesson 1 Homework Practice Volume Of Cylinders - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Answers lessons 12 1 and 12 2 name date period 8, Lesson 47 prisms and cylinders, Volumes of cylinders, , Practice a 10 6 volume of prisms and cylinders, Surface area prisms cylinders l1es1, By the mcgraw hill companies all rights, Lesson 47 prisms ...

Mon. January 12. Lesson: Surface Area of Prisms & Pyramids (Lesson Notes) Homework: Surface Area of Prisms & Pyramids (HOMEWORK w Answers) Fri. January 9. Lesson: Volume of Cylinders, Cones, & Spheres (Lesson Notes) Homework: Volume of Cylinders, Cones, & Spheres (Handout & Worksheet) Thurs. January 8. Lesson: Culminating Activity Work Period ...

Volume of cylinders, spheres, and cones word problems. Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27 π cm 3 of melted purple liquid. The radius of the cone is 3 cm. What is the height of the cone?

Description. In this 8th-grade volume homework resource, students will solve problems that involve finding the volume of cylinders, the volume of cones, and the volume of spheres. They will also have to solve questions where they are given the volume and must find the missing radius or height. They will also find the volume of composite solids.

This editable 7th grade math foldable provides students an organized set of practice problems for finding the volume and surface area of prisms and cylinders. The problems are organized as follows:Tab 1: Rectangular Prisms (#1 volume, #2 surface area)Tab 2: Triangular Prisms (#3 volume, #4 surface area)Tab 3: Cylinders (#5 volume, #6 surface ...

Maneuvering The Middle Llc 2016 Volume Of Cylinders - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Section volume of cylinders cones and spheres, Volumes of cones, Volume, Unit b homework helper answer key, Pythagorean theorem practice 1, 10 identifying solid figures, Scatter plots, Answer key ...