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Warm Up

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

  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. Problem of the Day A rectangular box is 3 ft. by 4 ft. by 12 ft. What is the distance from a top corner to the opposite bottom corner? 13 ft

  4. 8-3 Circles Learn to find the circumference and area of circles.

  5. Vocabulary circle radius diameter circumference

  6. A circle is the set of points in a plane that are a fixed distance from a given point, called the center. A radius connects the center to any point on the circle, and a diameter connects two points on the circle and passes through the center.

  7. 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.

  8. 22 7 Remember! Pi () is an irrational number that is often approximated by the rational numbers 3.14 and .

  9. 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

  10. 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.

  11. 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

  12. 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 m2

  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. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  15. Lesson Quiz for Student Response Systems 1. Find the circumference of a circle with a radius of 6.3 inches, both in terms of  and to the nearest tenth. Use 3.14 for . A.12.6 in.; 37.1 in. B.12.6 in.; 39.6 in. C.11.8 in.; 39.6 in. D.11.8 in.; 37.1 in.

  16. Lesson Quiz for Student Response Systems 2. Find the circumference of a circle with diameter of 120 mm, both in terms of  and to the nearest tenth. Use 3.14 for . A.120 mm; 376.8 mm B.240 mm; 753.6 mm C.240 mm; 376.8 mm D.120 mm; 753.6 mm

  17. Lesson Quiz for Student Response Systems 3. Find the of the circle with a radius of 2 mm, both in terms of  and to the nearest tenth. Use 3.14 for . A.4 mm; 6.3 mm B.4 mm; 12.6 mm C.2 mm; 6.2 mm D.2 mm; 12.6 mm

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