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.

Volume of a sphere = (4/3)πr^{3}

Volume of a right circular cone = (1/3)πr^{2}h

Volume of a cylinder = πr^{2}h

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 = (4/3)πr^{3} : πr^{2}h : (1/3)πr^{2}h

⇒ Ratio of their volumes = 4r^{3} : 6r^{3} : 2r^{3} = 2 : 3 : 1

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