Question

A sphere just fits inside a cube with edges 20 in. Long. What is the volume of the sphere? What is the volume of the cube? What is the volume of the space between the cube and sphere?

Answer 1

Explanation:

Volume of a cube = (side)³

= (20)³

= 8000 cubic in.

Volume of the sphere which just fits in =
`(4)/(3)\pi r^(3)`

Here, r = Radius of the sphere

Since, sphere just fits in, radius of the sphere = half of the dimension of the cube

r =
`(20)/(2)`

r = 10 in

Therefore, volume of the sphere =
`(4)/(3)\pi (10)^3`

= 4188.79 cubic inch

Volume of the space between the cube and sphere = 8000 - 4188.79

= 3811.21 cubic inch