Question

a sphere and a cube have equal surface areas. show that the ratio of their volume of a sphere to that of a cube is root over 6 :root over pie

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

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