Question

Ivan wants to fill with foam the empty space left in a cube-shaped box after he places a basketball in the box. How many cubic inches of foam is needed if the radius of the basketball is 4.75 in. and the sides of the box are each 9 in.? Use 3.14 for π, and round your answer to the nearest whole number. in.3

Answer 1

280 cubic inches

Explanation:

Cubic inches of foam required = volume of the box - volume of the basketball

The box has a shape of a cube, so that;

volume of the box =
`l^(3)`

where l is the length of the sides of the box.

volume of the box =
`9^(3)`

= 729 cubic inches

volume of the box = 729 cubic inches

The basketball has the shape of a sphere, so that;

volume of the basketball =
`(4)/(3)`
`\pi`
`r^(3)`

=
`(4)/(3)` x 3.14 x
`(4.75)^(3)`

= 448.693

volume of the basketball = 448.693 cubic inches

Thus,

cubic inches of foam required = 729 - 448.693

= 280.307

The cubic inches of foam to be used is 280 cubic inches.