Lesson 13: The Volume of a Cylinder

The Volume of a Cylinder

Student Summary

We can find the volume of a cylinder with radius $r$ and height $h$ using two ideas we've seen before:

The volume of a rectangular prism is the result of multiplying the area of its base by its height.
The base of the cylinder is a circle with radius $r$ , so the base area is $\pi r^2$ .

Remember that $\pi$ is the number we get when we divide the circumference of any circle by its diameter. The value of $\pi$ is approximately 3.14.

Just like a rectangular prism, the volume of a cylinder is the area of the base times the height. For example, consider a cylinder whose radius is 2 cm and whose height is 5 cm.

The base has an area of $4\pi$ cm² (since $\pi\boldcdot 2^2=4\pi$ ), so the volume is $20\pi$ cm³ (since $4\pi \boldcdot 5 = 20\pi$ ). Using 3.14 as an approximation for $\pi$ , we can say that the volume of the cylinder is approximately 62.8 cm³.

A drawing of a cylinder whose radius is 2 and height is 5.

In general, the base of a cylinder with radius $r$ units has area $\pi r^2$ square units. If the height is $h$ units, then the volume $V$ in cubic units is $V=\pi r^2h.$

Visual / Anchor Chart

Standards

Building On

6.G.2

Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

7.G.4

Apply the formulas for the area and circumference of a circle to solve problems.

Addressing

8.G.9

Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real world problems.