Question

A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is ______.

Options

• `sqrtpi : sqrt 6`

• `sqrt 6 : sqrt pi`

• `sqrt pi : sqrt 3`

• `sqrt 3 : sqrt pi`

Answer 1

A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is `underline(sqrt 6 : sqrt pi)`.

Explanation:

Let radius of sphere = r

and side of cube = x

∵ Surface Area of sphere = Surface Area of cube

`=> 4pi"r"^2 = 6 xx x^2`

`=> x = sqrt((2pi)/3)*"r"`

Volume of sphere = `4/3 pi"r"^3`

Volume of cube = `(sqrt((2pi)/3)*"r")^3`

`therefore "Required ratio" = 4/3 pi"r"^3 div (sqrt((2pi)/3)*"r")^3`

`= sqrt6 : sqrtpi`