EXAMPLE 2.7.7

Gomer delivers muffins for the Muffin-O-Matic muffin company. Each muffin is packed in its own little box. An individual muffin box has the shape of a cube, measuring 3 inches on each side. Gomer packs the individual muffin boxes into a larger box. The larger box is also in the shape of a cube, measuring 2 feet on each side. How many of the individual muffin boxes can fit into the larger box?

A. 8

B. 16

C. 64

D. 512

SOLUTION

To solve any problem that asks us "how many little objects are required to 'fill up' a bigger object?" we divide the size of the bigger object by the size of one of the smaller objects. Since these are three-dimensional objects, their size is their VOLUME. We will find the volume of the large box (in cubic inches) and divide by the volume an individual muffin box (in cubic inches).

The larger box is a cube measuring 24 inches by 24 inches by 24 inches, so its volume is

(24 inches) times (24 inches) times (24 inches) = 13,824 cubic inches.

An individual muffin box is a cube measuring 3 inches by 3 inches by 3 inches, so its volume is

(3 inches) times (3 inches) times (3 inches) = 27 cubic inches.

Thus, the number of smaller boxes need to fill the larger box is:

(volume of large box) divided by (volume of small box)

= (13,824 cubic inches) divided by (27 cubic inches) = 512

The large box can contain 512 of the small boxes.

The correct choice is D.