Question

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let the side of a cube be x

∴ Volume of a cube (V_c) = (x)³

Radius of a sphere `(r) = x/2`

Volume of sphere `(V_s) = 4/3 pi(r^3)`

= `4/3 pi (x/2)^3`

= `4/3 pi xx x^3/8`

∴ `V_c/V_s = x^3/(4/3 pi x^3/8) = 6/pi` or 6 : π

Hence, the required ratio is 6 : π.