Greenwood press

CIRCLES
13
A trundle wheel can be used to
measure long distances by mul-
tiplying the number of its revo-
lutions by its circumference.
The age of a tree is related to
the number of its rings and its
circumference.

---

with a diameter of 16 inches for $16. Is that a reasonable deal? Since the amount
of pizza is related to its area, it would be more beneficial if the consumer were
told the unit cost of the pizza per square inch. Instead, consumers may develop a
misconception and think that the 16-inch pizza should be 16/12, or 4/3, as much
as the 12-inch pizza. 
In the 12-inch pizza, the radius is 6 inches. So the area of the pizza is
π(6)
2
≈ 113.1 square inches. At a sale price of $10, the consumer is paying
about 8.8 cents per square inch of pizza. In the 16-inch pizza, the radius is 8
inches. So the area of the pizza is 
π(8)
2
≈ 201.1 square inches. At a sale price
of $16, the consumer is paying about 8.0 cents per square inch of pizza. At first
glance, one might think the 12-inch pizza is a better buy, but actually it is the
other way around. Since volume purchases usually have a cheaper unit price,
these prices seem pretty reasonable. Is this true about the prices at your favorite
pizza shop?
The area of a circle is helpful to farmers in determining the amount of space
that a sprinkling system will cover. As a sprinkler rotates, it will spray water in a
circular pattern, or in a sector of a circle if it is restricted in a certain way. The
distance the water reaches, or the radius of the circle, is sufficient information for
the farmer to determine how much space will be covered by the water and how
many sprinklers are needed to water the crops. Crops are often created in rectan-
gular grids to make harvesting easier, but watering in a rectangular pattern is
often less efficient than in a circular pattern. Therefore, the challenge in watering
crops is to determine how many circles can be packed into the rectangle region.
The trick for the farmer is to automate the sprinklers so that they provide just the
right amount of water to the crops to optimize production and minimize expense.
A circle is a figure that has an optimal area based on its perimeter. Based on
a given perimeter, there is not another shape that has an area greater than a cir-
cle. Similarly, based on a given area, there is not another shape that has a smaller
perimeter than a circle. In essence, this information indicates that a great way to
make use of materials and space is to form circles. Think about all the objects
made of raw materials that are shaped into circles, such as plates, cups, pots,
compact discs, and digital video discs. All of these objects are designed to hold
substances or information that take up space in a resourceful way. Parts of circles