9 2 Area of Circles Warm Up Problem

9 -2 Area of Circles Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

9 -2 Area of Circles Warm Up Simplify. 1. 82 64 2. 122 144 3. 6. 22 38. 44 4. 7. 52 56. 25

9 -2 Area of Circles 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.

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

9 -2 Area of Circles A circle can be cut into equalsized 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 = 1 Cr. 2 Since C = 2 r, A = 1 (2 r)r = r 2. 2

9 -2 Area of Circles

9 -2 Area of Circles Additional Example 1 A: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3. 14 for . A = r 2 7 cm Use the formula. A 3. 14 · 72 Substitute 7 for r. A 3. 14 · 49 Evaluate the power. Multiply. A 153. 86 The area of the circle is about 153. 9 cm 2. Remember! The order of operations calls for evaluating the exponents before multiplying.

9 -2 Area of Circles Additional Example 1 B: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3. 14 for . 18 ft A = r 2 Use the formula. A 3. 14 · 92 Substitute 9 for r. Evaluate the power. Multiply. A 3. 14 · 81 A 254. 34 The area of the circle is about 254. 3 ft 2.

9 -2 Area of Circles Check It Out: Example 1 A Find the area of the circle to the nearest tenth. Use 3. 14 for . 10 cm A = r 2 Use the formula. A 3. 14 · 102 Substitute 10 for r. Evaluate the power. Multiply. A 3. 14 · 100 A 314 The area of the circle is about 314 cm 2.

9 -2 Area of Circles Check It Out: Example 1 B Find the area of the circle to the nearest tenth. Use 3. 14 for . 12 ft A = r 2 Use the formula. A 3. 14 · 62 Substitute 6 for r. Evaluate the power. Multiply. A 3. 14 · 36 A 113. 04 The area of the circle is about 113. 0 ft 2.

9 -2 Area of Circles Additional Example 2: Application 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 22 for . cover the drain? Use 7 A = r 2 Use the formula for the area of a circle. A 22 · 142 Substitute. Use 14 for r. 7 28 A 22 · 196 Evaluate the power. 17 A 22 · 28 A 616 Multiply. The area of the top that will cover the drain is about 616 in 2.

9 -2 Area of Circles 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 22 for . cover that will be made? Use 7 A = r 2 A 22 · 72 7 7 A 22 · 49 17 A 22 · 7 A 154 Use the formula for the area of a circle. Substitute. Use 7 for r. Evaluate the power. Multiply. The area of the top that will cover spa is about 154 ft 2.

9 -2 Area of Circles Additional Example 3: Application Find the area of the shaded region of the circle. Use 3. 14 for . Round your answer to the nearest tenth. The measurement of the radius of the circle is 1. 5 cm Now find the area of the entire circle. A = r 2 Use the formula for the area of a circle. A = 3. 14 · 1. 52 Substitute. Use 1. 5 for r. A 3. 14 · 2. 25 Evaluate the power. A 7. 07 Multiply.

9 -2 Area of Circles Additional Example 3 Continued Find the area of the shaded region of the circle. Use 3. 14 for . Round your answer to the nearest tenth. 1 Since of the circle is shaded, divide the area of the 2 circle by 2. 7. 07 ÷ 2 = 3. 535. The area of the shaded region of the circle is about 3. 5 cm 2.

9 -2 Area of Circles Check It Out: Example 3 Find the area of the shaded region of the circle. Use 3. 14 for . Round your answer to the nearest tenth. The measurement of the radius of the circle is 2. 4 cm Now find the area of the entire circle. A = r 2 Use the formula for the area of a circle. A = 3. 14 · 2. 42 Substitute. Use 2. 4 for r. A 3. 14 · 5. 76 Evaluate the power. A 18. 09 Multiply.

9 -2 Area of Circles Check It Out: Example 3 Continued Find the area of the shaded region of the circle. Use 3. 14 for . Round your answer to the nearest tenth. 3 Since of the circle is shaded, divide the area of the 4 circle by 4 and subtract the answer from the entire area. 18. 0864 ÷ 4 = 4. 52. 18. 0864 – 4. 52 = 13. 56. The area of the shaded region of the circle is about 13. 56 cm 2.