Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm3

What is the volume of the sphere?

Answer 1

12 cm³

Explanation:

Let's say the radius of the sphere and cylinder is r and the height is h. However, notice that the "height" of the sphere is the same thing as the diameter, which is 2r, so h = 2r.

The volume of a sphere is denoted by:
`V=(4)/(3) \pi r^3` , where r is the radius.

The volume of a cylinder is denoted by:
`V=\pi r^2h`, where r is the radius and h is the height. Plug in 2r for h and 18 for V:

`V=\pi r^2h`

`18=\pi r^2*2r=2\pi r^3`

`\pi r^3=18/2=9`

Now plug in 9 for πr³ in the volume formula for the sphere:

`V=(4)/(3) \pi r^3`

`V=(4)/(3) *9=12`

The volume of the sphere is 12 cm³.