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

Volume of cylinder = πR².H

Volume Sphere: =4/3πR³

Volume of cylinder = Volume Sphere (given), then:

πR².H = 4/3πR³

Simplify==> R².H = (4/3)R³==>  H = (4/3)R===> R=3H/4