1. 10-5 Circles Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Warm Up The length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change. The perimeter is multiplied by 5, and the area is multiplied by 25. Course 1 10-5 Circles

3. Problem of the Day When using a calculator to find the height of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct height? 1.3 Course 1 10-5 Circles

4. Learn to identify the parts of a circle and to find the circumference and area of a circle. Course 1 10-5 Circles

5. Vocabulary circle center radius (radii) diameter circumference pi Insert Lesson Title Here Course 1 10-5 Circles

6. A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center Course 1 10-5 Circles

7. A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii). Center Radius Course 1 10-5 Circles

8. A chord is a line segment with both endpoints on a circle. A diameter is a chord that passes through the center of the circle. The length of the diameter is twice the length of the radius. Center Radius Diameter Course 1 10-5 Circles

9. Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. N The circle is circle Z.LM is a diameter.ZL, ZM, and ZN are radii. M Z L Course 1 10-5 Circles

10. Try This: Example 1 Name the circle, a diameter, and three radii. The circle is circle D.IG is a diameter.DI, DG, and DH are radii. G H D I Course 1 10-5 Circles

11. The distance around a circle is called the circumference. Center Radius Diameter Circumference Course 1 10-5 Circles

12. The ratio of the circumference to the diameter,, is the same for any circle. This ratio is represented by the Greek letter , which is read “pi.” C d C d =  Course 1 10-5 Circles

13. The formula for the circumference of a circle is C = d, or C = 2r. The decimal representation of pi starts with 3.14159265... and goes on forever without repeating. We estimate pi using either 3.14 or. 22 7 Course 1 10-5 Circles

14. Additional Example 2A: Using the Formula for the Circumference of a Circle Find the missing value to the nearest hundredth. Use 3.14 for pi. A. d = 11 ft; C = ? C = dC  3.14 11C  34.54 ft Write the formula. Replace  with 3.14 and d with 11. 11 ft Course 1 10-5 Circles

15. Additional Example 2B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. B. r = 5 cm; C = ? C = 2rC  2 3.14 5C  31.4 cm Write the formula. Replace  with 3.14 and r with 5. 5 cm Course 1 10-5 Circles

16. Additional Example 2C: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. C. C = 21.98 cm; d = ? C = d 21.98  3.14d7.00 cm  d Write the formula. Replace C with 21.98 and  with 3.14. 21.98 3.14d _______ 3.14 3.14  Divide both sides by 3.14. Course 1 10-5 Circles

17. Try This: Example 2A Find the missing value to the nearest hundredth. Use 3.14 for pi. A. d = 9 ft; C = ? C = dC  3.14 9C  28.26 ft Write the formula. Replace  with 3.14 and d with 9. 9 ft Course 1 10-5 Circles

18. Try This: Example 2B Find each missing value to the nearest hundredth. Use 3.14 for pi. B. r = 6 cm; C = ? C = 2rC  2 3.14 6C  37.68 cm Write the formula. Replace  with 3.14 and r with 6. 6 cm Course 1 10-5 Circles

19. Try This: Example 2C Find each missing value to the nearest hundredth. Use 3.14 for pi. C. C = 18.84 cm; d = ? C = d 18.84  3.14d6.00 cm  d Write the formula. Replace C with 18.84 and  with 3.14. 18.84 3.14d _______ 3.14 3.14  Divide both sides by 3.14. Course 1 10-5 Circles

20. The formula for the area of a circle is A = r 2. Course 1 10-5 Circles

21. Additional Example 3: Using the Formula for the Area of a Circle Find the area of the circle. Use for pi. d = 42 cm; A = ? Write the formula to find the area. A = r 2 r = d ÷ 2r = 42 ÷ 2 = 21 The length of the diameter is twice the length of the radius. Replace  with and r with 21. 22 7 __ A  441 22 7 __ Use the GCF to simplify. 63 A  1,386 cm 2 Multiply. 22 7 A  21 2 22 7 1 42 cm Course 1 10-5 Circles

22. Write the formula to find the area. A = r 2 r = d ÷ 2r = 28 ÷ 2 = 14 The length of the diameter is twice the length of the radius. Replace  with and r with 14. 22 7 __ A  196 22 7 __ Use the GCF to simplify. 28 A  616 cm 2 Multiply. Try This: Example 3 Find the area of the circle. Use for pi. d = 28 cm; A = ? 22 7 A  14 2 22 7 1 28 cm Course 1 10-5 Circles

23. Lesson Quiz Find the circumference and area of each circle. Use 3.14 for . 1. 2. 3. Find the area of a circle with a diameter of 20 feet. Use 3.14 for . C = 25.12 in. Insert Lesson Title Here C = 18.84 in. 8 in. 314 ft 2 A = 50.24 in 2 A = 28.26 in 2 3 in. Course 1 10-5 Circles