1. 9-5 Area of Circles Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Simplify. 1. 8 2 2. 12 2 3. 6.2 2 4. 7.5 2 64 144 38.44 56.25 Course 2 9-5 Area of Circles

3. Problem of the Day A 16 in. pizza sells for $11.99. A 10 in. pizza sells for $5.99. Which size gives you more pizza per penny? Explain. The larger pizza; you get more than twice as much (64 in 2 instead of 25 in 2 ) for about twice the price. Course 2 9-5 Area of Circles

4. Learn to find the area of circles. Course 2 9-5 Area of Circles

5. Course 2 9-5 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.

6. Course 2 9-5 Area of Circles AREA OF A CIRCLE The area A of a circle is the product of  and the square of the circle’s radius r. r A = r 2

7. Find the area of the circle to the nearest tenth. Use 3.14 for . Additional Example 1A: Finding the Area of a Circle Course 2 9-5 Area of Circles 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. The order of operations calls for evaluating the exponents before multiplying. Remember!

8. Find the area of the circle to the nearest tenth. Use 3.14 for . Additional Example 1B: Finding the Area of a Circle Course 2 9-5 Area of Circles 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.

9. Find the area of the circle to the nearest tenth. Use 3.14 for . Course 2 9-5 Area of Circles 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. Check It Out: Example 1A

10. Find the area of the circle to the nearest tenth. Use 3.14 for . Course 2 9-5 Area of Circles 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. Check It Out: Example 1B

11. 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 2: Application Course 2 9-5 Area of Circles 22 7 for . 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.

12. Course 2 9-5 Area of Circles 22 7 for . 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. Check It Out: Example 2 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? Use The area of the top that will cover spa is about 154 ft 2.

13. Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Additional Example 3: Application Course 2 9-5 Area of Circles A = r 2 A = 3.14 · 1.5 2 A  3.14 · 2.25 A  7.07 Use the formula for the area of a circle. Substitute. Use 1.5 for r. Evaluate the power. Multiply. The measurement of the radius of the circle is 1.5 cm. Now find the area of the entire circle. 1.5 cm

14. Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Additional Example 3 Continued Course 2 9-5 Area of Circles The area of the shaded region of the circle is about 3.5 cm 2. Since of the circle is shaded, divide the area of the circle by 2. 7.07 ÷ 2 = 3.535. 1212

15. Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Check It Out: Example 3 Course 2 9-5 Area of Circles A = r 2 A = 3.14 · 2.4 2 A  3.14 · 5.76 A  18.09 Use the formula for the area of a circle. Substitute. Use 2.4 for r. Evaluate the power. Multiply. The measurement of the radius of the circle is 2.4 cm. Now find the area of the entire circle. 2.4 cm

16. Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Check It Out: Example 3 Continued Course 2 9-5 Area of Circles The area of the shaded region of the circle is about 13.56 cm 2. Since of the circle is shaded, divide the area of the circle by 4 and subtract the answer from the entire area. 18.0864 ÷ 4 = 4.52. 18.0864 – 4.52 = 13.56. 3434

17. Lesson 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 a diameter of 2 in. What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for . 4. A round table cloth has a radius of 36 in. What is the area of the table cloth? Use 3.14 for . Round your answer to the nearest tenth. 63.6 ft 2 201.0 ft 2 Insert Lesson Title Here 3.1 in 2 4,069.4 in 2 Course 2 9-5 Area of Circles 2. 8 ft 9 ft