EXAMPLE 2.7.2

Gomer stores his iguana food in a can that is 8 inches tall and has a diameter of 6 inches. He stores his hamster food in a can that is 10 inches tall and has a diameter of 5 inches.

Which can is larger?

A. The iguana food can.

B. The hamster food can.

C. They are the same size.

D. There is insufficient information to answer this question.

SOLUTION

The size of a three-dimensional object corresponds to its volume, so we compare the volumes of these two objects. Each of these containers has the shape of a right circular cylinder. Recall the formula for the volume of a right circular cylinder:

Volume = pi times (radius squared) times height

 For the iguana food can, the height is 8 inches and the radius is 3 inches (half of diameter), so we have:

Volume = pi times (3 squared) times 8 = 72 pi cubic inches

For the hamster food can, the height is 10 inches and the radius is 2.5 inches (half of diameter), so we have:

Volume = pi times (3.5 squared) times 10 = 62.5 pi cubic inches

The iguana food can is largest.