volume of cylinders homework

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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

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Level : Advanced

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

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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.

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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.

Ellipsoid volume

Grams to cups, meat footprint, root mean square.

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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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Course: 8th grade   >   Unit 5

• Cylinder volume & surface area
• Volume of cylinders
• Volume of a sphere
• Volume of spheres
• Volume of a cone
• Volume of cones

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 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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: 13 May, 2024].

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HW Volume of Prisms & cylinders

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

20 January 2015

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