Basic Math Operations - Mathematics and Statistics for the Environment - page 63

6 ft

12 ft

FIGURE 2.6 Area of a circle for Example 2.47.

where
A = Area.
π = pi = 3.14.
r = Radius of circle = one half of the diameter.

■ EXAMPLE 2.47
Problem: What is the area of the circle shown in Figure 2.6?

Solution:

Area of circle = π × r 2 = π × 6 2 = 3.14 × 36 = 113 ft 2

If we are assigned to paint a water storage tank, we must know the surface area of the walls of the
tank to determine how much paint is required. In this case, we need to know the area of a circular
or cylindrical tank. To determine the surface area of the tank, we need to visualize the cylindrical
walls as a rectangle wrapped around a circular base. The area of a rectangle is found by multiplying
the length by the width; in the case of a cylinder, the width of the rectangle is the height of the wall,
and the length of the rectangle is the distance around the circle (circumference).
Thus, the area ( A ) of the side wall of a circular tank is found by multiplying the circumference of
the base ( C = π × D ) times the height of the wall ( H ):

A = π × D × H (2.8)

A = π × 20 ft × 25 ft = 3.14 × 20 ft × 25 ft = 1570 ft 2

To determine the amount of paint needed, remember to add the surface area of the top of the tank,
which is 314 ft 2 . Thus, the amount of paint needed must cover 1570 ft 2 + 314 ft 2 = 1884 ft 2 . If the
tank floor should be painted, add another 314 ft 2 .
Many ponds are watershed ponds that have been built by damming valleys. These ponds are
irregular in shape. If no good records exist on the pond, then a reasonable estimate can be made
by chaining or pacing off the pond margins and using the following procedures to calculate area:

1. Draw the general shape of the pond on graph paper.

2. Draw a rectangle over the pond shape that would approximate the area of the pond if some
water was eliminated and placed onto an equal amount of land. This will give you a rect-
angle on which to base the calculation of area (see Figure 2.7).