Question

A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

Answer 1

Volume of a sphere = \(\frac{4}{3}\)πr³ 

Volume of a right circular cone = \(\frac{1}{3}\)πr²h 

Volume of a cylinder = πr²h

Given, 

sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere

Height of cone and cylinder = 2r

Ratio of their volumes =   \(\frac{4}{3}\)πr³ : πr²h :\(\frac{1}{3}\)πr²h 

⇒ Ratio of their volumes = 4r³ : 6r³ : 2r³ 

= 2 : 3 : 1