1. Perimeter and Area with Circles

2. Circumference of a Circle Circumference is the perimeter of the circle Formula: or (for exact answers, leave π in your answer, for estimates, use the π key)

3. Example Find the circumference of a circle with a radius of 16 inches. inches

4. Example Find the circumference of the given circle. C = π d C = π (10) cm C = 10 π cm

5. Arc length is the length, of a piece, of the circle. Use a proportion that related part to whole, one side is length, the other side is degree measure. arc length = arc measure circumference 360 Arc Length

6. Radian Measure Radian measure is the arc length in the unit circle (a circle with radius of 1)

7. Example In Circle P, find the length of arc AB C = 20 π or 13.96 cm

8. Example In Circle G, with diameter 12 cm, find the length of C = 12 π Arc = 3 π cm

9. Shortcut Since 90° is 1/4 th of the circle, you can find the circumference and divide it by 4. C = 12 π Arc = 12 π /4 = 3 π cm

10. Example Convert 90° to radians. Convert 150° to radians. Convert 315° to radians (answers on the next slide)

11. Answers

12. Area of a circle Formula:

13. Example Find the area of a circle with a radius of 10 mm. mm 2

14. Example Find the Area of the Circle Radius = 20 cm cm 2

15. Area of a Sector The area of a sector is the area of a wedge shaped piece of the circle. You use a proportion just like the one for arc length

16. Example Find the area of the shaded sector of Circle O with radius 30 cm (for circle) cm 2