Question

a cube and sphere has equal total surface area find the ratio of the volume of Sphere and cube

Answer 1

Let r and a be the radius of the sphere and edge of the cube respectively.

Given, Surface area of sphere = Surface area of cube

4πr2 = 6a2

(r/a)2 = 3 / 2π

r / a = √(3/2π)

Volume of sphere / Volume of cube = (4/3)πr3 / a3 = (4π/3)(r/a)3

= (4π/3)(√(3/2π))3

= (4π/3)(3/2π)(√(3/2π))

= 2√(3/2π)

= √(4x3/2π)

= √(6/π)

Thus, Volume of sphere : Volume of cube = √6 : √π.  

Answer 2

Let r and a be the radius of the sphere and edge of the cube respectively.
Given, Surface area of sphere = Surface area of cube
4πr2 = 6a2
(r/a)2 = 3 / 2π
r / a = √(3/2π)
Volume of sphere / Volume of cube = (4/3)πr3 / a3 = (4π/3)(r/a)3
= (4π/3)(√(3/2π))3
= (4π/3)(3/2π)(√(3/2π))
= 2√(3/2π)
= √(4x3/2π)
= √(6/π)
Thus, Volume of sphere : Volume of cube = √6 : √π.  


hope this helps u....