Question

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let r be the radius of the sphere and cylinder.

Given that height of the cylinder = diameter of the sphere.

`\implies` h = 2r

According to the question,

Volume of a sphere = `2/3` × volume of cylinder

`\implies 4/3 pir^3 = 2/3 xx pir^2 xx 2r`  ...[∵ h = 2r]

`\implies 4/3 pir^3 = 4/3 pir^3`

Hence, the volume of a sphere is equal to two-third of the volume of a cylinder.