Question

A sphere of a cube have a some
surface area show that the ratio
of the volume of sphere: volume of cube
root 6: root5
​

Answer 1

Correct question :

A sphere of a cube have a some surface area show that the ratio of the volume of sphere: volume of cube √6 : √π

Solution :

Let the radius of the sphere be 'r' units and

edge of the cube be 'a' units.

Given that,

Surface area of the sphere = Surface area of

the cube

= 4πr² = 6a²

= r²/a² = 6/4π

= 3/2π

= r/a = (3/2π)½ ........ (1)

= volume of sphere/volume of cube

= 4/3πr³/a³

= 4/3π(r/a)³

= 4/3π (3/2π)^3/2

= 4/3π x 3/2π√3/2π6

= 2√3/2π

= √3 x 2²/2π

= √6/√π

= √6 : √π .............hence proved