9-2 Area of Circles
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
9-2 Area of Circles
Warm Up
Simplify.
1. 82
64
2. 122
144
3. 6.22
38.44
4. 7.52
56.25
9-2 Area of Circles
Problem of the Day
A 16 in. pizza sells for $11.99. A 10 in.
pizza sells for $5.99. Which size gives you
more pizza per penny? Explain.
The larger pizza; you get more than
twice as much (64 in2 instead of 25 in2)
for about twice the price.
9-2 Area of Circles
I can find the area of circles.
9-2 Area of Circles
A circle can be cut into equalsized sectors and arranged to
resemble a parallelogram. The
height h of the parallelogram is
equal to the radius r of the circle,
and the base b of the
parallelogram is equal to one-half
the circumference C of the circle.
So the area of the parallelogram can be written as
A = bh, or A = 1 Cr.
2
Since C = 2r, A = 1 (2r)r = r2.
2
9-2 Area of Circles
9-2 Area of Circles
Additional Example 1A: Finding the Area of a Circle
Find the area of the circle to the nearest tenth.
Use 3.14 for .
A = r2
7 cm
Use the formula.
A  3.14 · 72
Substitute 7 for r.
A  3.14 · 49
Evaluate the power.
Multiply.
A  153.86
The area of the circle is about 153.9 cm2.
Remember!
The order of operations calls for evaluating the
exponents before multiplying.
9-2 Area of Circles
Additional Example 1B: Finding the Area of a Circle
Find the area of the circle to the nearest tenth.
Use 3.14 for .
18 ft
A = r2
Use the formula.
A  3.14 · 92
Substitute 9 for r.
Evaluate the power.
Multiply.
A  3.14 · 81
A  254.34
The area of the circle is about 254.3 ft2.
9-2 Area of Circles
Check It Out: Example 1A
Find the area of the circle to the nearest tenth.
Use 3.14 for .
10 cm
A = r2
Use the formula.
A  3.14 · 102
Substitute 10 for r.
Evaluate the power.
Multiply.
A  3.14 · 100
A  314
The area of the circle is about 314 cm2.
9-2 Area of Circles
Check It Out: Example 1B
Find the area of the circle to the nearest tenth.
Use 3.14 for .
12 ft
A = r2
Use the formula.
A  3.14 · 62
Substitute 6 for r.
Evaluate the power.
Multiply.
A  3.14 · 36
A  113.04
The area of the circle is about 113.0 ft2.
9-2 Area of Circles
Additional Example 2: Application
Park employees are fitting a top over a
circular drain in the park. If the radius of the
drain is 14 inches, what is the area of the top
that will cover the drain? Use 22 for .
7
A =  r2
Use the formula for the area of a circle.
A  22 ·142
Substitute. Use 14 for r.
7
28
A  22 ·196
Evaluate the power.
17
A  22 · 28
A  616
Multiply.
The area of the top that will cover the drain is about 616 in2.
9-2 Area of Circles
Check It Out: Example 2
Albert was designing a cover for a spa. If the
radius of the spa is 7 ft, what is the area of
the cover that will be made? Use 22 for .
7
A =  r2
A  22 ·72
7
7
A  22 · 49
17
A  22 · 7
A  154
Use the formula for the area of a circle.
Substitute. Use 7 for r.
Evaluate the power.
Multiply.
The area of the top that will cover spa is about 154 ft2.
9-2 Area of Circles
Additional Example 3: Application
Find the area of the shaded region of the
circle. Use 3.14 for  . Round your answer to
the nearest tenth.
The measurement of the radius of the
circle is 1.5 cm.
1.5 cm
Now find the area of the entire circle.
A = r2
Use the formula for the area of a circle.
A = 3.14 · 1.52
Substitute. Use 1.5 for r.
A  3.14 · 2.25
Evaluate the power.
A  7.07
Multiply.
9-2 Area of Circles
Additional Example 3 Continued
Find the area of the shaded region of the
circle. Use 3.14 for  . Round your answer to
the nearest tenth.
1
Since of the circle is shaded, divide the area of the
2
circle by 2. 7.07 ÷ 2 = 3.535.
The area of the shaded region of the circle is about
3.5 cm2.
9-2 Area of Circles
Check It Out: Example 3
Find the area of the shaded region of the
circle. Use 3.14 for  . Round your answer to
the nearest tenth.
The measurement of the radius of the
circle is 2.4 cm.
2.4 cm
Now find the area of the entire circle.
A = r2
Use the formula for the area of a circle.
A = 3.14 · 2.42
Substitute. Use 2.4 for r.
A  3.14 · 5.76
Evaluate the power.
A  18.09
Multiply.
9-2 Area of Circles
Check It Out: Example 3 Continued
Find the area of the shaded region of the
circle. Use 3.14 for  . Round your answer to
the nearest tenth.
3
Since of the circle is shaded, divide the area of the
4
circle by 4 and subtract the answer from the entire area.
18.0864 ÷ 4 = 4.52. 18.0864 – 4.52 = 13.56.
The area of the shaded region of the circle is about
13.56 cm2.