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)(24 inches)(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)(3 inches)(3 inches) = 27 cubic inches.
Thus, the number of smaller boxes need to fill the larger box is:
The correct choice is D.