Question

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

What is the volume of the sphere?

Answer 1

Formulas for calculating:

sphere's volume -
`V_(sphere)=(4\pi r^3)/(3)`;

cylinder's volume -
`V_(cylinder)=\pi r^2h` .

Note that h=2r (height of the sphere consists of two radius).

Then
`V_(cylinder)=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3` .

Since
`V_(sphere)=(4\pi r^3)/(3)` you have that
`\pi r^3=(3V_(sphere))/(4)` and
`V_(cylinder)=2\pi r^3=2\cdot (3V_(sphere))/(4)=(3V_(sphere))/(2)` .

You have only to substitute correct number for
`V_(sphere)`.