Question

If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.

Answer 1

In the given problem, we are given a sphere inscribed in a cube. So, here we need to find the ratio between the volume of a cube and volume of sphere. This means that the diameter of the sphere will be equal to the side of the cube. Let us take the diameter as d.

Here,

Volume of a cube (V₁) = s³ 

= d³ 

Volume of a sphere (V₂) `=(4/3)pi (d/2)^3`

`=(4/3) pi (d^3/8)`

`=(pid^3)/6`

Now, the ratio of the volume of sphere to the volume of the cube = `V_1/V_2`

`V_1/V_2 = d^3/(((pi d^3)/6))`

               `= 6/pi`

So, the ratio of the volume of cube to the volume of the sphere is `6 : pi` .