Volume of a Cylinder: Formula & Examples

Let’s learn how to determine the volume of a cylinder.

What is a Cylinder?

A cylinder is a tube-shaped object with two same-sized circular bases, parallel straight sides, and a circular or oval cross-section. Its height is the distance between the two bases, while the radius is the distance from the center of a base to any point on the same base. Examples of cylinder-shaped objects are soda cans and pipes. 

Related Reading: Surface Area of a Cylinder – Formula & Examples

How to Find the Volume of a Cylinder:

You may recall that the volume of a three-dimensional shape refers to the amount of space it occupies.

To find a cylinder’s volume, multiply the cylinder’s base and height, as expressed in this formula: 

V=Bh  or  V=πr²h where B (Base)=πr² ; h=height ; π=3.14

Since the cylinder has circular bases, the Area formula of a circle ( A= πr² ) is used to find the cylinder’s volume. Like other three-dimensional shapes, the volume of a cylinder is measured in cubic units such as cubic inch (in³), cubic feet (ft³), cubic centimeter (cm³), or cubic meter (m³).

Here’s a quick guide to finding the volume of a cylinder:

Step 1. Write down the given figures. You’ll need the cylinder’s radius and height. Make sure all measurement units are the same. If not, convert either of them to match the other. 

Step 2. Plug the figures into the formula.

Step 3. Perform the operations. Don’t forget to write the cubit unit together with the answer.

Example 1: Finding the Volume of a Cylinder when given Height and Radius

Find the volume of the cylinder below.

Solution for Example 1:

Write down the given figures, the radius (r = 2m) and height (h = 3m).

Substitute 2m for r and 3m for h in the formula.

V=πr²h

V=π(2m)²(3m)

Simplify.

V=π(4m²)(3m)

V=π(12m³)

V=37.68m³

Therefore, the volume is 37.68m³.

Example 2: Finding the Volume of a Cylinder when given Height and Diameter

Find the volume of the cylinder below.

Solution for Example 2:

Write down the given figures, the diameter (d = 3m) and height (h = 125cm). Recall that the formula requires the radius and not the diameter. So, divide the diameter (3m) by 2 to find the radius.

r = d/2 = 3m/2 = 1.5m

Now let’s convert the height (125cm) to match the radius’ unit (m). Remember that 100cm = 1m.

h = 125cm/100cm = 1.25m

Substitute 1.5m for r and 1.25m for h in the formula.

V=πr²h

V=π(1.5m)²(1.25m)

Simplify.

V=π(2.25m²)(1.25m)

V=π(2.8125m³)

V=8.83125m³

Therefore, the volume is about 8.83m³.

Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the volume of a cylinder.

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