Question

A cylinder is placed within a cube. The diameter of the cylinder is equal to the length of each side of the cube. What is the volume of the space outside the cylinder and inside the cube if the side of the cube measures 8 inches?

Cube with a cylinder inside it. The sides of the cube and the diameter of the cylinder are all 8 inches.

Group of answer choices

110 cubic inches

384 cubic inches

100 cubic inches

1,097 cubic inches

Answer 1

Option a (110 cubic inches) is the right solution.

Explanation:

Given:

Diameter of cylinder,

= 8 inches

Radius,

= 4 inches

Now,

The volume of space will be:

=
`Volume \ of \ cube - Volume \ of \ cylinder`

=
`(Side)^3 - \pi r^2 h`

=
`(8)^3 - (22)/(7)* (4)^2* 8`

=
`512-(22)/(7)* 128`

=
`512-4.0`

=
`110 \ cubic \ inches`