1. 6-4 Circles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation 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? Course 3 6-4 Circles 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? Course 3 6-4 Circles 13 ft

4. Learn to find the area and circumference of circles. Course 3 6-4 Circles

5. Course 3 6-4 Circles circle radius diameter circumference Vocabulary

6. Course 3 6-4 Circles 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. Course 3 6-4 Circles Radius Center Diameter Circumference The diameter d is twice the radius r. d = 2r The circumference of a circle is the distance around the circle.

8. Course 3 6-4 Circles

9. Course 3 6-4 Circles Remember! Pi () is an irrational number that is often approximated by the rational numbers 3.14 and. 22 7

10. Course 3 6-4 Circles Additional Example 1: Finding the Circumference of a Circle 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 Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .

11. Course 3 6-4 Circles Try This: Example 1 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. Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .

12. Course 3 6-4 Circles

13. Course 3 6-4 Circles Additional Example 2: Finding the Area of a Circle A = r 2 = (4 2 ) = 16in 2  50.2 in 2 A. Circle with a radius of 4 in. Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . B. Circle with a diameter of 3.3 m A = r 2 = (1.65 2 ) = 2.7225 m 2  8.5 m 2 d2d2 = 1.65

14. Course 3 6-4 Circles B. Circle with a diameter of 2.2 ft A = r 2 = (1.1 2 ) = 1.21ft 2  3.8 m 2 d2d2 = 1.1 Try This: Example 2 Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . A = r 2 = (8 2 ) = 64cm 2  201.0 cm 2 A. Circle with a radius of 8 cm

15. Course 3 6-4 Circles Additional Example 3: Finding the Area and Circumference on a Coordinate Plane A = r 2 = (3 2 ) = 9units 2  28.3 units 2 C = d = (6) = 6units  18.8 units 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 

16. Course 3 6-4 Circles Try This: Example 3 x y A = r 2 = (4 2 ) (–2, 1) = 16units 2  50.2 units 2 C = d = (8) = 8units  25.1 units 4 (–2, 5) 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 

17. Course 3 6-4 Circles Additional Example 4: Measurement Application C = d = (56)  176 ft  (56)  22 7 22 7 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. 56 1 22 7 The distance is the circumference of the wheel times the number of revolutions, or about 176  15 = 2640 ft.

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

19. Course 3 6-4 Circles Lesson Quiz Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for . 1. radius 5.6 m 2. diameter 113 m 11.2m; 35.2 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. 4. diameter 1 ft 9in 2 ; 28.3 in 2 0.25ft 2 ; 0.8 ft 2