Volume of a Cylinder

Grade 8 Math Worksheets

Let’s begin at the beginning and define a cylinder. It is a solid surrounded by two parallel planes and a cylinder. It can be visualized as a real container with top and bottom lids. Its radius (or diameter) and height are the two variables we need to know in order to compute its volume:

Cylinder volume = π × cylinder radius² × cylinder height

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Volume of a Cylinder Worksheet PDF

This is a free worksheet with practice problems and answers. You can also work on it online.

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Types of Cylinder

Using this formula, where B is the area of the base and h is the height, you can determine the volume of a cylinder.

V=Bh

You can rewrite the formula as follows to indicate that the area of the base is simply the area of either circular face.

V=𝜋r2h

Try it out! Find the cylinder’s volume. Use 3.14 as a rough estimate for. Use to denote “roughly equal to” since you’re using an approximation for.

V= 62 4

V= 364

V=144

V3.14144

V452.16

So, the volume of the cylinder is approximately 452.16 cubic centimeters!

Another Example

Let’s try another example. This time you know the diameter. Remember that the diameter is twice the radius. Find the volume of the cylinder. Use 3.14 as an approximation for 𝜋.

Start by finding the radius. You can find the radius by dividing the diameter by 2.

10 2 =5

So, the radius is 5 inches. Now we are ready to plug into our formula.

V= 52 12

V= 2512

V=300

V3.14144

V942

So, the volume of the cylinder is approximately 942 cubic inches!

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Finding the Radius

You can use the volume formula to find the radius of a cylinder if you know its volume. Let’s try it! The volume of this cylinder is approximately

615.44 cubic meters. Find the radius. Use 3.14 as an approximation for 𝜋.

V=𝜋r2h

When Volume of Cylinder =615.44 cubic centimeters height =4 centimeters.

V= 3.14 r2 4

615.44= r2 4

615.443.14 r2 4

615.44r212.56

615.4412.56 r2

r249

r=7

So, the radius of the cylinder is 7 meters!

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FAQs

Are there any units for volume?

Yes, the units for volume are cubic units. For example, if the radius and height are in centimeters, the volume will be in cubic centimeters (cm³).

Do I need to use the value of π (pi) in the formula?

Yes, it’s important to use the value of π in the formula for accurate calculations. You can use an approximate value like 3.14 or use the π button on a calculator for more precision.

What if the cylinder is slanted or tilted?

The volume formula assumes the cylinder has a straight axis. If the cylinder is slanted or tilted, you may need additional information to calculate the volume. In some cases, you might use calculus or other geometric methods.

Can the height of the cylinder be negative?

In a geometric context, height is a distance and is typically considered positive. However, in certain physics or real-world applications, the height could be negative if you’re measuring displacement in a different direction.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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