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

Answer:

280 cubic inches

Step-by-step 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 = $\frac{4}{3}$ $\pi$$r^{3}$

                                          = $\frac{4}{3}$ 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.