Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 64m. What is the volume of the sphere

Answer 1

check the picture below.


`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} h=2r\\ V=64 \end{cases}\implies 64=\pi r^2(2r)\implies 64=3\pi r^3\implies \boxed{\cfrac{64}{3\pi }=r^3}\\\\ -------------------------------\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \boxed{(64)/(3\pi )} \right)}{3}\implies V=\cfrac{256}{9}`