Question

26. Find the ratio of the volume of a cube to that of the sphere which fits inside the cube.​

Answer 1

For sphere to fit exactly in cube it’s radius should be equal to a/2 where a is side length of cube.

Volume of cube / Volume of Sphere = a³ / (4πr³/3)

= a³ / (4π × (a³/8) / 3) ……[∵ r = a/2]

= 6a³ / (πa³)

= 6 / π

Ratio is 6 : π