1. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 1 Chapter 9 Geometry

2. CHAPTER Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 2 9 Geometry 9.1Perimeter 9.2Area 9.3Circles 9.4Volume 9.5Angles and Triangles 9.6Square Roots and the Pythagorean Theorem

3. OBJECTIVES Copyright © 2015, 2011, and 2008 Pearson Education, Inc. 3 9.3 Circles aFind the length of a radius of a circle given the length of a diameter, and find the length of a diameter given the length of a radius. bFind the circumference of a circle given the length of a diameter or a radius. cFind the area of a circle given the length of a diameter or a radius. dSolve applied problems involving circles.

4. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 4 Segment is a diameter. A diameter is a segment that passes through the center of the circle and has endpoints on the circle. Segment is called a radius. A radius is a segment with one endpoint on the center and the other endpoint on the circle. r B A C O d

5. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 5 Diameter and Radius Suppose that d is the diameter of a circle and r is the radius. Then d = 2  r and

6. 6 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the length of a radius of this circle. Solution 16 m The radius is 8 m.

7. 7 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the length of a diameter of this circle. Solution ½ ft The diameter is 1 ft.

8. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 8 The perimeter of a circle is called its circumference. Circumference and Diameter The circumference C of a circle of diameter d is given by The number is about 3.14, or about

9. 9 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the circumference of this circle. Use 3.14 for . Solution 8 m

10. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 10 Circumference and Radius The circumference C of a circle of radius r is given by

11. 11 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the circumference of this circle. Use 22/7 for . Solution 140 in.

12. 12 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the perimeter of this figure. Use 3.14 for . Solution We let P = the perimeter. Since there is 1/2 a circle replacing the fourth side of a square, we add half the circumference to the lengths of the three line segments. 5.2 km 8.2 km 5.6 km

13. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 13 Area of a Circle The area of a circle with radius of length r is given by r

14. 14 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the area of this circle. Use 3.14 for . Round to the nearest hundredth. Solution 3.6 m

15. 15 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example A local pizza parlor is ordering new square serving plates. If they order a 16 in. plate how much area will show when a 14 in. diameter pizza is placed on the pan? Familiarize. Look at the drawing, notice that the corners of the box will be visible when the pizza is in place. We let A = the area of the box visible. 14 in.

16. 16 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. continued Translate. Area of box minus Area of pizza is Visible Area s  s –   r  r = A Solve. The radius is ½ the diameter, or 7 in. s  s –   r  r = A 16 in.  16 in. – 3.14  7 in.  7 in.  A 256 in 2 – 153.86 in 2  A 102.14 in 2  A

17. 17 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. continued Check. We can check by repeating our calculations. Note also that the area of the plate does not exceed the area of the pizza. State. When the pizza is in place, about 102.14 in 2 of plate will be visible.