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

Explanation

Let radius of sphere = r and side of cube = a units According to ques, Surface area of sphere = Surface area of cube => 4πr2 = 6a2 r2 3 => a2 = 2π r 3 3 3 => ( a ) = ( 2π ) 2 ∴ Volume of sphere : Volume of cube 4 3 πr3 4π r = a3 = ( 3 )( a )3 2 2π 3 3 = 3 ( 2π ) 2 3 3 (2) 2− 2 (3) 2 −1 3 = (π) 2 −1 1 1 (2) 2 (3) 2 1 = (π) 2 = 6: π