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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up 1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long. 2. The hypotenuse of a right triangle measures 17 in., and one leg measures 8 in. How long is the other leg?

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up • 1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long. • 2. The hypotenuse of a right triangle measures 17 in., and one leg measures 8 in. How long is the other leg? • 3. To the nearest centimeter, what is the height of an equilateral triangle with sides 9 cm long? 5 in. 15 in. 8 cm

  3. California Standards MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered:MG3.2

  4. Vocabulary circumference

  5. Circumference Radius Center The diameter d is twice the radius r. Diameter d= 2r The circumference of a circle is the distance around the circle.

  6. 22 7 Remember! Pi () is an irrational number that is often approximated by the rational numbers 3.14 and .

  7. Additional Example 1: Finding the Circumference of a Circle Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . A. circle with a radius of 4 m C = 2r = 2(4) = 8 m  25.1 m B. circle with a diameter of 3.3 ft C = d =  (3.3) = 3.3 ft  10.4 ft

  8. Check It Out! Example 1 Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . A. circle with a radius of 8 cm C = 2r = 2(8) = 16 cm  50.2 cm B. circle with a diameter of 4.25 in. C = d = (4.25) = 4.25 in.  13.3 in.

  9. d 2 = 1.65 Additional Example 2: Finding the Area of a Circle Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . A. circle with a radius of 4 in. A = r2 = (42) = 16 in2 50.2 in2 B. circle with a diameter of 3.3 m A = r2 = (1.652) = 2.7225 m2 8.5 m2

  10. d 2 = 1.1 Check It Out! Example 2 Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . A. circle with a radius of 8 cm A = r2 =  (82) = 64 cm2 201.0 cm2 B. circle with a diameter of 2.2 ft A = r2 =  (1.12) = 1.21 ft2 3.8 ft2

  11. Additional Example 3: Finding the Area and Circumference on a Coordinate Plane Graph the circle with center (–2, 1) that passes through (1, 1). Find the area and circumference, both in terms of  and to the nearest tenth. Use 3.14 for . C = d A = r2 = (6) = (32) = 6 units = 9 units2  18.8 units  28.3 units2

  12. y (–2, 1) Check It Out! Example 3 Graph the circle with center (–2, 1) that passes through (–2, 5). Find the area and circumference, both in terms of  and to the nearest tenth. Use 3.14 for . A = r2 C = d (–2, 5) = (42) = (8) = 16 units2 4 = 8 units  50.2 units2  25.1 units x

  13. 22 7 22 7  (56)  56 1 22 7 Additional Example 4: Measurement Application A Ferris wheel has a diameter of 56 feet and makes 15 revolutions per ride. How far would someone travel during a ride? Use for . Find the circumference. C = d = (56)  176 ft The distance is the circumference of the wheel times the number of revolutions, or about 176  15 = 2640 ft.

  14. 22 7 12 22 7  (14)  9 3 14 1 22 7 6 Check It Out! Example 4 A second hand on a clock is 7 in. long. What is the distance it travels in one hour? Use for . C = d =  (14) Find the circumference.  44 in. The distance is the circumference of the clock times the number of revolutions, or about 44  60 = 2640 in.

  15. Lesson Quiz Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . 11.2 m; 35.2 m 1. radius 5.6 m 2. diameter 113 m 113 mm; 354.8 mm Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . 3. radius 3 in. 9 in2; 28.3 in2 0.25 ft2; 0.8 ft2 4. diameter 1 ft

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