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2-14-13 Circumference and Area of Circles EQ: What are the parts of a circle?

2-14-13 Circumference and Area of Circles EQ: What are the parts of a circle? How can we find the diameter of a circle if we know the circumference or area? How can we find the radius of a circle if we know the circumference or area? . BOP :. DWP: .

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2-14-13 Circumference and Area of Circles EQ: What are the parts of a circle?

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  1. 2-14-13 Circumference and Area of Circles EQ: What are the parts of a circle? How can we find the diameter of a circle if we know the circumference or area? How can we find the radius of a circle if we know the circumference or area? BOP: DWP:

  2. 2-14-13 Circumference and Area of Circles EQ: What are the parts of a circle? How can we find the diameter of a circle if we know the circumference or area? How can we find the radius of a circle if we know the circumference or area? BOP: Evaluate the following expressions. 1 2 1. · 6 · 8 24 1 2 2. · 5.4 · 7.2 19.44 3. 4(7 + 10) 68 4. 3.5(12 + 8.2) 70.7

  3. Use a compass to draw a circle. RADIUS CHORD DIAMETER

  4. 8-6 Circumference of Circles Course 2 CIRCUMFERENCEOF A CIRCLE d The circumference of a circle is times the diameter. r •

  5. 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 •

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 8-5 Area of Triangles and Trapezoids Course 2 Insert Lesson Title Here Lesson Quiz Find the area of each figure. 1. 3. 9 in2 2. 3 in. 45 ft2 9 ft 6 in. 10 ft 10 ft 8 ft 4. 87.5 ft2 7 ft 60 ft2 6 ft 15 ft 12 ft 4. What is the height of a triangle with area 36 cm2 and a base 9 cm? 8 cm

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 8-5 Area of Triangles and Trapezoids Course 2 Insert Lesson Title Here Lesson Quiz Find the area of each figure. 1. 3. 9 in2 2. 3 in. 45 ft2 9 ft 6 in. 10 ft 10 ft 8 ft 4. 87.5 ft2 7 ft 60 ft2 6 ft 15 ft 12 ft 4. What is the height of a triangle with area 36 cm2 and a base 9 cm? 8 cm

  23. 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

  24. Hand papers back that were started yesterday with area and perimeter of rectangles and triangles. Make corrections to work. Do the circle problems. Name the shape Write the formula Substitute Solve Add units

  25. 10.

  26. Summary: What new information have you found out about circles? Homework: WBW #1 is due on Friday. Be sure to show all work. Study vocabulary and formulas.

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