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 - $V_{sphere}=\dfrac{4\pi r^3}{3}$;

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 $V_{sphere}=\dfrac{4\pi r^3}{3}$ you have that $\pi r^3=\dfrac{3V_{sphere}}{4}$ and $V_{cylinder}=2\pi r^3=2\cdot \dfrac{3V_{sphere}}{4}=\dfrac{3V_{sphere}}{2}$ .

You have only to substitute correct number for $V_{sphere}$.