Basic Mathematics for College Students

9.8 Circles 797

Self Check 4

Find the area of the shaded

figure below. Round to the

nearest hundredth.

Now TryProblem 37

26 yd

10 yd

24 yd

8 in.

6 in.

10 in.

EXAMPLE (^4) Find the area of the shaded figure
on the right. Round to the nearest hundredth.
StrategyWe will find the area of the entire shaded
figure using the following approach:
WHYThe shaded figure is a combination of a triangular
region and two semicircular regions.
SolutionThe area of the triangle is
Since the formula for the area of a circle is , the formula for the area of a
semicircle is. Thus, the area enclosed by the smaller semicircle is
The area enclosed by the larger semicircle is
The total area is the sum of the three results:
Use a calculator to
perform the operations.
To the nearest hundredth, the area of the shaded figure is 88.40 in.^2.
Atotal 24  8 p12.5p88.4026494
Alarger semicircle

1

2

pr^2 

1

2

p( 5 )^2 

1

2

p(25)12.5p

Asmaller semicircle

1

2

pr^2 

1

2

p( 4 )^2 

1

2

p(16) 8 p

A^12 pr^2

Apr^2

Atriangle

1

2

bh

1

2

( 6 )( 8 )

1

2

(48) 24

AtotalAtriangleAsmaller semicircleAlarger semicircle

1. 24 p m75.4 m 2.39.42 m 3. 36 p ft^2 113.1 ft^2 4.424.73 yd^2

ANSWERS TO SELF CHECKS

Using Your CALCULATOR Painting a Helicopter Landing Pad

Orange paint is available in gallon containers

at $19 each, and each gallon will cover

375 ft^2. To calculate how much the paint

will cost to cover a circular helicopter

landing pad 60 feet in diameter, we first

calculate the area of the helicopter pad.

This is the formula for the area of a circle.

Substitute one-half of 60 for r, the radius of the circular pad.

Write the product so that Pis the last factor.

The area of the pad is exactly ft^2. Since each gallon of paint will cover 375 ft^2 ,

we can find the number of gallons of paint needed by dividing by 375.

We can use a scientific calculator to make this calculation.

30 375

Because paint comes only in full gallons, the painter will need to purchase

8 gallons. The cost of the paint will be 8($19), or $152.

x^2  p    7.539822369

Number of gallons needed

302 p

375

302 p

302 p

 302 p

Ap( 30 )^2

Apr^2

12.5

2  25.0

 2

05

 4

10

 10

0