Circumference, Area, and Volume - Basic Mathematics for Water and Wastewater Operators - page 164

14 ft

6 ft 6 ft

14 ft

FIGURE 11.6 Illustration for Example 11.8.

■ Example 11.8
Problem: Find the area of the rectangle shown in Figure 11.6.

Solution:

Area = L × W = 14 ft × 6 ft = 84 ft 2

a rea of a C irCle
In order to calculate volumes of circular tanks and velocities in pipes, the area of the
circle must first be determined. There are two basic formulas used to calculate the
area of a circle.

Area of circle = π × r 2 (11.4)

Area of circle = 0.785 × D 2 (11.5)

where
π = pi = 3.14.
r = Radius of circle = one-half of the diameter.
D = Diameter.

The radius ( r ) is any straight line that radiates form the center of the circle to some
point on the circumference. By definition, all radii of the same circle are equal. The
area of a circle is determined by multiplying π times the radius squared. In Figure
11.7, we have a circle with a radius of 6 inches.

6 ft

12 ft

FIGURE 11.7 Illustration of area of a circle.