Question

Determine the ratio of the volume of a cube to that of a sphere which will fit exactly inside the cube

Answer 1

let edge of cube is x.
radius of sphere =edge of square/2
=x/2
volume of cube =edge ^ 3
=x ^ 3
volume of sphere =4/ 3pie*r ^
=4/ 3*22/7*x/2*x/2*x/2
=11/21x ^ 3

volume of cube:volume of sphere
=x ^ 3: 11/21 x ^ 3
=21: 11

Answer 2

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

If ′l′′l′ is the side of the cube , then

Volume of the cube (V1)=l3(V1)=l3

Volume of the sphere (V2)=43π(l2)3(V2)=43π(l2)3
∴V1:V2∴V1:V2 is l3:43π(l2)3l3:43π(l2)3
l3:43πl38l3:43πl38
l3:πl36l3:πl36
6:π6:π