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

Options

•  π : 2

•  π : 3

• π : 4

• π : 6

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 sphere and volume of a cube. 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 sphere (V₁) =  `(4/3) pi (d/2)^3`

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

=`(pi d^3)/6`

Volume of a cube (V₂) = S³ 

`=d^3`

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

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

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