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

2. Holt CA Course 1 10-5 Area of Circles VOCABULARY Area of Circles Formula

3. Holt CA Course 1 10-5 Area 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 = 1212 Cr. Since C = 2  r, A = 1212 (2  r)r =  r 2.

4. Holt CA Course 1 10-5 Area of Circles

5. Holt CA Course 1 10-5 Area of Circles Find the area of the circle by using a formula. Then use an estimate to check whether your answer is reasonable. Teacher Example 1: Estimation Application A = r 2 A  3.14 · 3 2 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.

6. Holt CA Course 1 10-5 Area of Circles Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable. Teacher 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.

7. Holt CA Course 1 10-5 Area of Circles Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable. Student Practice 1: A = r 2 A  3.14 · 2 2 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.

8. Holt CA Course 1 10-5 Area of Circles Find the area of the circle by using a formula. then use an estimate to check whether your answer is reasonable. Student Practice 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.

9. Holt CA Course 1 10-5 Area of Circles A. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . Teacher Example 2A: Finding the Area of a Circle 7 cm A =  r 2 A  3.14 · 7 2 A  3.14 · 49 A  153.86 The area of the circle is about 153.9 cm 2. Use the formula. Substitute 7 for r. Evaluate the power. Multiply.

10. Holt CA Course 1 10-5 Area of Circles B. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . Teacher Example 2B: Finding the Area of a Circle 18 ft A =  r 2 A  3.14 · 9 2 A  3.14 · 81 A  254.34 The area of the circle is about 254.3 ft 2. Use the formula. Substitute 9 for r. Evaluate the power. Multiply.

11. Holt CA Course 1 10-5 Area of Circles A. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . 10 cm A =  r 2 A  3.14 · 10 2 A  3.14 · 100 A  314 The area of the circle is about 314 cm 2. Use the formula. Substitute 10 for r. Evaluate the power. Multiply. Student Practice 2A:

12. Holt CA Course 1 10-5 Area of Circles B. Find the area of the circle to the nearest tenth. Use 3.14 as an estimate for . 12 ft A =  r 2 A  3.14 · 6 2 A  3.14 · 36 A  113.04 The area of the circle is about 113.0 ft 2. Use the formula. Substitute 6 for r. Evaluate the power. Multiply. Student Practice 2B:

13. Holt CA Course 1 10-5 Area 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? Teacher Example 3: Application A =  r 2 A  22 7 ·14 2 A  22 7 · 196 A  22 · 28 A  616 The area of the top that will cover the drain is about 616 in 2. 1 28 Use the formula for the area of a circle. Substitute. Use 14 for r. Evaluate the power. Multiply.

14. Holt CA Course 1 10-5 Area of Circles A =  r 2 A  22 7 ·72·72 A  22 7 · 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. Student Practice 3: 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? The area of the top that will cover spa is about 154 ft 2.

15. Holt CA Course 1 10-5 Area of Circles 10.5 Warm-Up Find the area of each circle to the nearest tenth. Use 3.14 for . 1. 2. 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 . 8 ft