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8-6

8-6. Area of Circles. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 8-6. Area of Circles. Course 2. Warm Up Simplify. 1. 8 2 2. 12 2 3. 6.2 2 4. 7.5 2. 64. 144. 38.44. 56.25. 8-6. Area of Circles. Course 2. Problem of the Day

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8-6

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  1. 8-6 Area of Circles Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 8-6 Area of Circles Course 2 Warm Up Simplify. 1.82 2. 122 3. 6.22 4. 7.52 64 144 38.44 56.25

  3. 8-6 Area of Circles Course 2 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 in2 instead of 25in2) for about twice the price.

  4. 8-6 Area of Circles Course 2 Learn tofind the area of circles.

  5. 8-6 Area of Circles Course 2 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 1 2 Cr. A = bh, or A = 1 2 Since C = 2r, A = (2r)r = r2.

  6. 8-6 Area of Circles Course 2 AREA OF A CIRCLE The area A of a circle is the product of and the square of the circle’s radius r. A = r2 r •

  7. 8-6 Area of Circles Remember! The order of operations calls for evaluating the exponents before multiplying. Course 2 Additional Example 1A: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 A. Use the formula. 7 cm 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 cm2.

  8. 8-6 Area of Circles Course 2 Additional Example 1B: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 B. Use the formula. A 3.14 · 92 Substitute 9 for r. 18 ft A 3.14 · 81 Evaluate the power. Multiply. A  254.34 The area of the circle is about 254.3 ft2.

  9. 8-6 Area of Circles Course 2 Try This: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 A. Use the formula. A 3.14 · 102 10 cm Substitute 10 for r. A 3.14 · 100 Evaluate the power. Multiply. A  314 The area of the circle is about 314 cm2.

  10. 8-6 Area of Circles Course 2 Try This: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 B. Use the formula. 12 ft A 3.14 · 62 Substitute 6 for r. A 3.14 · 36 Evaluate the power. Multiply. A  113.04 The area of the circle is about 113.0 ft2.

  11. 8-6 Area of Circles Course 2 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 cover the drain? Use 22 7 for . A = r2 Use the formula for the area of a circle. 22 7 ·142 Substitute. Use 14 for r. A  28 22 7 196 · A  Evaluate the power. 1 A 22 · 28 Multiply. A 616 The area of the top that will cover the drain is about 616 in2.

  12. 8-6 Area of Circles Course 2 Try This: 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 22 7 for . A = r2 Use the formula for the area of a circle. 22 7 ·72 A  Substitute. Use 7 for r. 7 22 7 49 · A  Evaluate the power. 1 A 22 · 7 Multiply. A 154 The area of the top that will cover spa is about 154 ft2.

  13. 8-6 Area of Circles Course 2 Additional Example 3: Application A golf course is irrigated with sprinklers that spray in a circle. If a sprinkler waters a circular area with a radius of 25 feet, how many square feet does the sprinkler cover? Round your answer to the nearest whole number. A =  r2 Use the formula for the area of a circle. A = · 252 Substitute. Use 25 for r. Use a calculator. A  1963.495408 25   x2 Round. A 1,963 The sprinkler covers about 1,963 ft2.

  14. 8-6 Area of Circles Course 2 Try This: Example 3 Janet had a circular fish pond in her back yard. She wanted to find the surface area of the pond. If it had a radius of 13 feet, what is its surface area in square feet? Round your answer to the nearest whole number. A =  r2 Use the formula for the area of a circle. A = · 132 Substitute. Use 13 for r. Use a calculator. A  530.9216 13   x2 Round. A 531 The pond has a surface area of about 531 ft2.

  15. 8-6 Area of Circles Course 2 Insert Lesson Title Here 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. 2. 9 ft 8 ft • • 201.0 ft2 63.6 ft2 3.1 in2 4,069.4 in2

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