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Lesson 7.2

Lesson 7.2. Objective: To find area and circumference of circles . Diameter. Center. Circumference. Radius. Circumference. You can find the circumference if you know the diameter (d) or the radius (r) of the circle. Example. Find the circumference of a circle with a radius of 8.

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Lesson 7.2

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  1. Lesson 7.2 Objective: To find area and circumference of circles. Diameter Center Circumference Radius

  2. Circumference You can find the circumference if you know the diameter (d) or the radius (r) of the circle. Lesson 7.2 Area and Circumference

  3. Example Find the circumference of a circle with a radius of 8. This is the circumference “in terms of pi”. When computing C in decimal, use 3.14 or the pi button. Lesson 7.2 Area and Circumference

  4. Semicircle • Half of a circle. • Its measure is 180. • Its length is one-half the circumference. Lesson 7.2 Area and Circumference

  5. Problem 1 An indoor track at a gym has the design below. What is the length of the entire track? 40 ft 100 ft Lesson 7.2 Area and Circumference

  6. Problem 1 Solution The ends make one circle. The diameter is 40 ft. C = (40) 40 ft 100 ft Lesson 7.2 Area and Circumference

  7. Problem 1 Solution Add 200 for the straight segments. Perimeter = 40 + 200 ft Or, 325.66 ft. 40 ft 100 ft Lesson 7.2 Area and Circumference

  8. Area of a Circle r Lesson 7.2 Area and Circumference

  9. Example Find the area of the circle. Solution: A = (72) = 49 in2 or A  153.94 in2 7 in Lesson 7.2 Area and Circumference

  10. EX: Find the area of the shaded region Find the area of the square and circle. Subtract the area of the circle from the area of the square 20 m Area of square 20 X 20 = 400 Area of the circle Square – circle 400 – 314 Lesson 7.2 Area and Circumference

  11. Example At Moldy Cheese Pizza they sell two sizes of pizza: medium and large. The medium has a diameter of 10 inches and the large has a diameter of 16 inches. On Fridays they have a special: you get one large pizza, or two medium pizzas for the same price. Which is the better deal? Lesson 7.2 Area and Circumference

  12. Large Radius = 8 Area = ? Medium Radius = 5 Area = ? 64 25 5 8 Lesson 7.2 Area and Circumference

  13. Large Area = 64 Medium Area = 25 5 8 Lesson 7.2 Area and Circumference

  14. Large Area = 64 Medium Area = 25 So two medium pizzas have an area of 50 8 5 5 Lesson 7.2 Area and Circumference

  15. Solution: Buying one large has more area than two mediums. 64 8 25 25 201 in2 5 5 157 in2 Lesson 7.2 Area and Circumference

  16. Problem To water a square yard, a man installs four sprinkler heads as shown. The sprinkler heads spray water in a circular pattern with a radius of 4 feet. After a while, he notices some the grass is dying. What is the area of the yard that doesn’t get any water? 4 ft Lesson 7.2 Area and Circumference

  17. Problem Solution Area of square A = 162 = 256 ft2 Area of one circle A = (42) = 16 ft2 Area of four circles A = 4(16) = 64 A  201 ft2 4 ft 16 ft ? 8 ft ? 16 ft ? Dying Area 256 – 201 = 55 ft2 Lesson 7.2 Area and Circumference

  18. Your Turn Find the area of the (ring) – the shaded region. 2 in 5 in Lesson 7.2 Area and Circumference

  19. Solution Find the area of the (ring). Area of Outer Circle Radius = 7 in. Area = 49 Area of Inner Circle Radius = 5 Area = 25 25 2 in 5 in 7 49 Lesson 7.2 Area and Circumference

  20. Solution Outer Circle Area = 49 Inner Circle Area = 25 Area Outer – Inner = 49 - 25 = 24  75.4 in2 25 2 in 5 in 49 Lesson 7.2 Area and Circumference

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