Question

a display box is designed to hold a single baseball so the ball touches all six faces of the box. if the diameter is 2.9 inches, how much empty space is in the box around the ball.

Answer 1

11.619 cubic inches empty space is in the box around the ball.

Explanation:

We are given diameter of the ball in the empty box = 2.9 inches.

So, the each side of the box is 2.9 inches.

Radius of the ball = 2.9/2 = 1.45 inches.

Volume of the complete box without ball =
`(Side)^3`.

Plugging value of side in above formula, we get

Volume of the empty box =
`(2.9)^3.`=24.389 cubic inches.

Volume of the ball = volume of the sphere with radius 1.45 inches =
`(4)/(3) \pi r^3`.

=
`(4)/(3) \pi (1.45)^3` =
`(12.1945\pi )/(3)`

= 12.77.

Therefore, volume of the empty box around the ball = Volume of box-volume of ball = 24.389 - 12.77 = 11.619 cubic inches.

11.619 cubic inches empty space is in the box around the ball.