Question

If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.

Answer 1

Radius of sphere$=2r$

Radius of cone$=r$

Volume of sphere$=\frac{4}{3}\pi (2{)}^3=\frac{32}{3}\pi r^3$

Volume of cone$=\frac{1}{3}\times \pi r^{2}h\frac{\pi r^{2}h}{3}$

Given volume of sphere and cone are equal.

$\therefore \frac{32\pi r^3}{3}=\frac{\pi r^{2}h}{3}$

$h=32r$.