Question

A sphere amd a cube have the same surfave ffind the ratio of tje volumes

Answer 1

Let radius of sphere be R and side of cube be S.

Surface areas are 4πR² and 6S² (assuming total surface area)

So, 4πR² = 6S²

⇒ R/S = √(6/(4π))

⇒ R/S = √(3/(2π))

Volumes are 4/3 * πR³ and S³

So ratio = (4/3* πR³):S³

            = 4/3 *π (R/S)³

           =  4/3* π (√(3/(2π))) ³

          = 4/3 *π *(√(3/(2π)))*(3/(2π))

          = 2√(3/(2π))

          =√(6/π)