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Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson Presentation Preview Preview
Holt CA Course 1
10-5Area of Circles
Warm UpWarm UpCalifornia StandardsCalifornia StandardsLesson PresentationLesson Presentation
PreviewPreview
Holt CA Course 1
10-5Area of Circles
Warm UpSimplify.
1. 82
2. 122
3. 6.22
4. 7.52
6414438.4456.25
Holt CA Course 1
10-5Area of Circles
MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.Also covered: AF3.1, AF3.2, t MG1.1
California Standards
227
Holt CA Course 1
10-5Area of CirclesA circle can be cut into equal-sized 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 = 12
Cr.
Since C = 2r, A = 12
(2r)r = r2.
Holt CA Course 1
10-5Area of Circles
Holt CA Course 1
10-5Area of Circles
Find the area of the circle by using a formula. Then use an estimate to check whether your answer is reasonable.
Additional Example 1: Estimation Application
A = r2
A 3.14 · 32
A 3.14 · 9 A 28.26 square units
Use the formula.
Use 3.14 as an estimate for , and use 3 for r.
Evaluate the power.
Multiply.
Holt CA Course 1
10-5Area of Circles
Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable.
Additional Example 1 Continued
16 + 8 + ½(8) = 28 square units
16 squares are completely inside the circle. 8 squares are mostly inside the circle.
Because 28 is close to 28.26, an answer of 28.26 square units is reasonable.
Check Use the grid to estimate the area.
8 squares are halfway inside the circle.
Holt CA Course 1
10-5Area of Circles
Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable.
Check It Out! Example 1
A = r2
A 3.14 · 22
A 3.14 · 4 A 12.56
Use the formula.
Use 3.14 as an estimate for , and use 2 for r.
Evaluate the power.
Multiply.
Holt CA Course 1
10-5Area of Circles
Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable.
Check It Out! Example 1 Continued
4 + 8 + = 12 square units
4 squares are completely inside the circle. 8 squares are mostly inside the circle.
Because 12 is close to 12.56, an answer of 12.56 square units is reasonable.
Check Use the grid to estimate the area.
Holt CA Course 1
10-5Area of Circles
A. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for .
Additional Example 2: Finding the Area of a Circle
7 cmA = r2
A 3.14 · 72
A 3.14 · 49A 153.86
The area of the circle is about 153.9 cm2.
Use the formula.Substitute 7 for r.Evaluate the power.Multiply.
Holt CA Course 1
10-5Area of Circles
B. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for .
Additional Example 2: Finding the Area of a Circle
18 ftA = r2
A 3.14 · 92
A 3.14 · 81A 254.34
The area of the circle is about 254.3 ft2.
Use the formula.Substitute 9 for r.Evaluate the power.Multiply.
Holt CA Course 1
10-5Area of Circles
A. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for .
10 cmA = r2
A 3.14 · 102
A 3.14 · 100A 314
The area of the circle is about 314 cm2.
Use the formula.Substitute 10 for r.Evaluate the power.Multiply.
Check It Out! Example 2
Holt CA Course 1
10-5Area of Circles
B. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for .
12 ft
A = r2
A 3.14 · 62
A 3.14 · 36A 113.04
The area of the circle is about 113.0 ft2.
Use the formula.Substitute 6 for r.Evaluate the power.Multiply.
Check It Out! Example 2
Holt CA Course 1
10-5Area of CirclesPark 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
Additional Example 3: Application
227 as an estimate for .
A = r2
A 227 ·142
A 227
·196
A 22 · 28A 616
The area of the top that will cover the drain is about 616 in2.
128
Use the formula for the area of a circle.Substitute. Use 14 for r.
Evaluate the power.
Multiply.
Holt CA Course 1
10-5Area of Circles
227
A = r2
A 227 ·72
A 227
· 49
A 22 · 7A 154
17
Use the formula for the area of a circle.Substitute. Use 7 for r.
Evaluate the power.
Multiply.
Check It Out! Example 3Albert 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 as an estimate of .
The area of the top that will cover spa is about 154 ft2.
Holt CA Course 1
10-5Area of CirclesLesson Quiz
Find the area of each circle to the nearest tenth. Use 3.14 for .1.
3. The bull’s-eye on a target has diameter 2 in.What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for .
4. A round tablecloth has a radius of 36 in. What isthe area of the table cloth? Use 3.14 for . Roundyour answer to the nearest tenth.
63.6 ft2201.0 ft2
3.1 in2
4,069.4 in2
2.8 ft 9 ft• •
