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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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 area of circles; compare with actual measurements. Also covered: AF3.1, AF3.2, t MG1.1 California Standards 22 7

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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