Question

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is :

A. π : 2 

B. π : 3 

C. π : 4 

D. π : 6

Answer 1

Option : (D) 

Volume of a cube = side³ 

Volume of a sphere = \(\frac{4}{3}\)πr³ 

Given, 

sphere is inscribed in a cube 

Diameter of sphere = side of the cube 

Side of cube = 2r 

Ratio of the volume of the sphere to the volume of cube

= \(\frac{\frac{4}{3}\pi r^3}{(2r)^3}\) 

= π : 6