Question

A designer is planning a trail mix box that is shaped like a rectangular prism. The front of the box must have the width and height shown. Volume of the box must be 162 cubic inches. What must be the depth, d, of the box?

Answer 1

The box must be 2.4 in deep.

Explanation:

Front dimensions are 9 in by 7.5 in. Find the area of the front: it is

A = (9 in)(7.5 in) = 67.5 in^2. One way to complete this work would be to divide the given volume by this area, 67.5 in^2.

A slightly different approach follows:

The volume must be 162 in^2. Given V = (width)(height)(depth),

V

(depth) must be -----------------------

(width)(height)

In this particular case,

162 in^3

(depth) must be ----------------------- = 2.4 in

(7.5 in)(9 in)

The box must be 2.4 in deep.