Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards...
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Transcript of Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards...
![Page 1: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/1.jpg)
Holt CA Course 1
10-5Area of Circles
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
![Page 2: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/2.jpg)
Holt CA Course 1
10-5Area of Circles
Warm UpSimplify.
1. 82
2. 122
3. 6.22
4. 7.52
64
144
38.44
56.25
![Page 3: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/3.jpg)
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
![Page 4: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/4.jpg)
Holt CA Course 1
10-5Area of Circles
A 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.
![Page 5: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/5.jpg)
Holt CA Course 1
10-5Area of Circles
![Page 6: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/6.jpg)
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.
![Page 7: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/7.jpg)
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.
![Page 8: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/8.jpg)
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 cm
A = r2
A 3.14 · 72
A 3.14 · 49
A 153.86
The area of the circle is about 153.9 cm2.
Use the formula.
Substitute 7 for r.Evaluate the power.Multiply.
![Page 9: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/9.jpg)
Holt CA Course 1
10-5Area of Circles
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
Additional Example 3: Application
227
as an estimate for .A = r2
A 227
·142
A 227
·196
A 22 · 28
A 616
The area of the top that will cover the drain is about 616 in2.
1
28
Use the formula for the area of a circle.
Substitute. Use 14 for r.
Evaluate the power.
Multiply.
![Page 10: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/10.jpg)
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.
![Page 11: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/11.jpg)
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.
![Page 12: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/12.jpg)
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 cm
A = r2
A 3.14 · 102
A 3.14 · 100
A 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
![Page 13: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/13.jpg)
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 · 36
A 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
![Page 14: Holt CA Course 1 10-5 Area of Circles Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e615503460f94b5cf1d/html5/thumbnails/14.jpg)
Holt CA Course 1
10-5Area of Circles
227
A = r2
A 227
·72
A 227
· 49
A 22 · 7
A 154
1
7
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.
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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• •