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.
Radius of sphere$$=2r$$
Radius of cone$$=r$$
Volume of sphere$$=\dfrac{4}{3}\pi(2)^3=\dfrac{32}{3}\pi r^3$$
Volume of cone$$=\dfrac{1}{3}\times \pi r^2h\dfrac{\pi r^2h}{3}$$
Given volume of sphere and cone are equal.
$$\therefore \dfrac{32\pi r^3}{3}=\dfrac{\pi r^2h}{3}$$
$$h=32r$$.