Question

find the ratio of the volumes of a cube to that of a sphere which will exactly fit inside the cube

Answer 1

The sphere which exactly fits into the cube will have the diameter as the same as the side of the cube.

If ′l′ is the side of the cube , then

Volume of the cube (V1)=l3

Volume of the sphere (V2)=43π(l2)3

∴V1:V2 is l3:43π(l2)3

⟹l3:43πl38

⟹l3:πl36

⟹6:π