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Pizza Size Comparison: More Pizza Per Penny

This lesson teaches students how to find the area of circles and apply it to real-life scenarios. It includes a problem of the day, a lesson presentation, quizzes, and a warm-up activity.

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Pizza Size Comparison: More Pizza Per Penny

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Presentation Transcript

  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Simplify. 1. 82 2. 122 3. 6.22 4. 7.52 64 144 38.44 56.25

  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 in2 instead of 25in2) for about twice the price.

  4. I can find the area of circles.

  5. 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. Remember! The order of operations calls for evaluating the exponents before multiplying. 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 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.

  7. 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 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.

  8. Check It Out: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 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.

  9. Check It Out: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 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.

  10. 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.

  11. 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 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.

  12. 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. 1.5 cm The measurement of the radius of the circle is 1.5 cm. Now find the area of the entire circle. A = r2 Use the formula for the area of a circle. Substitute. Use 1.5 for r. A = 3.14 · 1.52 A  3.14 · 2.25 Evaluate the power. Multiply. A 7.07

  13. 1 2 Since of the circle is shaded, divide the area of the circle by 2. 7.07 ÷ 2 = 3.535. 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. The area of the shaded region of the circle is about 3.5 cm2.

  14. 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. 2.4 cm The measurement of the radius of the circle is 2.4 cm. Now find the area of the entire circle. A = r2 Use the formula for the area of a circle. Substitute. Use 2.4 for r. A = 3.14 · 2.42 A  3.14 · 5.76 Evaluate the power. Multiply. A 18.09

  15. 3 4 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. 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. The area of the shaded region of the circle is about 13.56 cm2.

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