1. Proportions in Circles
Area of a Sector and Arch Length

2. Practice Find the area and circumference of the following circles:
r = 1.5 (round to nearest hundredth)
d = 17
C = 22
A = 17.3 (round to nearest hundredth)

3. Review Area of a Circle = Π is Circumference of a Circle =
What does it mean to find the EXACT measurement of something?

4. Area of a sector How many degrees are in a circle?
How many degrees are in the sector?
Set up a proportion based on the total area.

5. Area of a sector
The angle of a wedge in a circle is 45 degrees. The radius of the circle is 1.
What fraction of the circle’s area is the wedge?
What is the exact area of the circle?
What is the exact area of the wedge?
Use two common approximations for π to find the area of the wedge.

6. Find the area of the sector

7. Practice HW: pg. 647, #4-10

8. Arcs of Circles
Arc AB
Minor arc
Major arc

9. Arc Length L is the length of the arc C is the circumference
The Central Angle is also the degree measure of the arc.
Set up a proportion using the Central Angle measure and L and C.

10. Find the measure of the Central Angle
L is 2Π
L is Π

11. What’s a radian?
There are 360 degrees in a circle – no one knows the exact origin…the Babylonians used a base-60 number system so that may have led to the 60 degrees in a equilateral triangle....however,
There are other ways to measure angles. The ration of arc length to radius defines a measure of angle called the RADIAN.
Radian – the measure in radians of a central angle of a circle is the ration L/r of the intercepted arc length L to the circle’s radius r.

12. What is the measure of each central angle in radians?
L = pi
r = 5
L = 2pi

13. Practice: HW pg 659, #7-14