1. 8.7 Circumference and Area of Circles

2. Definition  A circle is the set of all points in a plane that are the same distance from a given point, called the center of the circle.  A circle with center is called “circle,” or.

3. Terms  The distance from the center to a point on the circle is the radius.  The distance across the circle, through the center, is the diameter.  The circumference of a circle is the distance around the circle.

4. Terms  radius  diameter  circumference r d c

5. Terms  For any circle, the ratio of the circumference to its diameter is denoted by the Greek letter π, or pi.  The number π is 3.14159…, which is an irrational number, which neither terminates nor repeats.  An approximation of 3.14 is used for π.

6. Circumference of a Circle  Words  Circumference = π (diameter) = 2π (radius)  Symbols  C = πd or C = 2πr

7. Finding Circumference  Find the circumference of the circle. 4 in. C = πd or C = 2πr C = 2πr = 2π(4) = 8π = 8(3.14) = 25.12 in.

8. Area of a Circle  Words  Area = π (radius) 2  Symbols  A = πr 2

9. Finding Area of a Circle  Find the Area of the Circle A = πr 2 A = π(7) 2 A = π(49) A = (3.14)(49) A = 153.94 cm 2 7 cm

10. Using the Area of a Circle Find the radius of a circle with an area of 380 square feet. A = πr 2 380 = πr 2 380/ π = r² 120.96 ≈ r² 11 ft ≈ r r

11. Central Angles An angle whose vertex is the center of a circle is a central angle of the circle. A region of a circle determined by two radii and a part of the circle is called a sector of the circle. r ө

12. Central Angles Because a sector is a portion of a circle, the following proportion can be used to find the area of a sector. r Area sector Area circle Measure central angle Measure circle = ө