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Radius of a cylinder from volume

Teaching Transcript

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Find the radius of this cylinder from it's volume and its height

The volume of any prism, including a cylinder, is just the area of its base times the length of the straight sides. In this case the straight sides are its height

We know the volume is 36 pi, and the height is 4

So we can rearrange and find the area of the base is 9 pi

The area of a circle is pi times the radius squared, so we can equate that to 9 pi

Cancelling out the factors of pi, we can see that the radius squared is 9

So the radius must be 3

This math skill teaches how to determine the radius of a cylinder given its volume and height. Using the formula for the volume of a cylinder (volume = area of base × height), you rearrange the equation to find the base area first. Then, equate the base area to the formula for the area of a circle to solve for the radius.

Skill Practice

Radius of a cylinder from volume and height

Test your understanding of radius of a cylinder from volume by practicing it! Work through the below exercises to use it in practice.