Question

A sphere and a right cylinder have the same radius and volume. Find the radius r in terms of the height h of the cylinder.

Answer 1

`r=(3)/(4)h`

Explanation:

we know that

The volume of the sphere is equal to

`V=(4)/(3)\pi r^(3)` ----> equation A

The volume of the right cylinder is equal to

`V=\pi r^(2)h` ----> equation B

equate equation A and equation B

`(4)/(3)\pi r^(3)=\pi r^(2)h`

Simplify

`(4)/(3)r=h`

`r=(3)/(4)h`