Question

A basketball with a diameter of 9.5 in. is placed in a cubic box with sides 15 in. long. How many cubic inches of packing foam are needed to fill the rest of the box? Round to the nearest tenth.

Answer 1

2926.32 cubic inches

Explanation:

Given the information:

• A basketball with a diameter of 9.5 in

=> its radius is: 9.5/2 = 4.75 in

As we know, the formula used to find the volume of the sphere is:

V =π
`(4)/(3) r^(3)`

=> the volume of the basketball is:

V = π
`(4)/(3) 4.75^(3)`

= 448.69 cubic inches

• A cubic box with sides 15 in

As we know, the formula used to find the volume of a cube is:

V =
`a^(3)`

=> the volume of the box:

V =
`15^(3)` = 3375 cubic inches

Hence, The volume of foam there is needed to complete the box is the subtraction between the two volumes above:

= the volume of the box - the volume of the basketball

= 3375 - 448.69

= 2926.32 cubic inches