Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values...
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Transcript of Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values...
![Page 1: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/1.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 2: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/2.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 3: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/3.jpg)
Holt CA Course 1
10-5Area of Circles
![Page 4: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/4.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 5: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/5.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 6: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/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.
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 7: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/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.
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 8: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/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 MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/9.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 .
Additional Example 2: Finding the Area of a Circle
18 ft
A = r2
A 3.14 · 92
A 3.14 · 81
A 254.34
The area of the circle is about 254.3 ft2.
Use the formula.
Substitute 9 for r.Evaluate the power.Multiply.
![Page 10: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/10.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 11: Holt CA Course 1 10-5 Area of Circles MG1.2 Know common estimates of (3.14; ) and use these values to estimate and calculate the circumference and the.](https://reader035.fdocuments.us/reader035/viewer/2022072013/56649e615503460f94b5ceed/html5/thumbnails/11.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