**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.

**Solution:**

True

Let the radius of the sphere and cylinder be r.

Given, height of the cylinder = diameter of the base => h = 2r

According to the given condition,

Volume of sphere = (2/3) x Volume of cylinder

4/3 πr3 = (4/3) x πr2 x 2r

4/3 πr3 = 4/3 πr3

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