1. Objectives Derive the formula for area of a circle
Find arc lengths and the area of sectors using both degrees and radians.

2. Area of a Circle Proof
Workbook pg 503
The formula for circumference is C = 2r
The formula for area of a circle is A = r2
Recall

3. Example 1
The General Sherman tree in Sequoia National Park, CA is considered the worlds largest tree. The tree is approximately circular at its base, with a circumference of 102.6ft. What is the approximate diameter of the tree? What is the approximate area of a cross section at the base? Round each answer to the nearest foot.

4. Turn to workbook page 504
Highlight the definition of a sector and the formula for area of a sector
Complete example 2

5. In the same way that the area of a sector is a fraction of the area of the circle, the length of an arc is a fraction of the circumference of the circle.
Highlight the definition of arc length and the formula for arc length on workbook pg 505
Complete pg 505 example 3

6. Example 4
A windshield wiper blade is 18 inches long. To the nearest square inch, what is the area covered by the blade as it rotates through an angle of 122°?

7. Degrees versus Radians
Angles of a circle can be measured in degrees out of 360o.
Another unit used to measure angles of a circle is radians.
2π radians = 360o = 1 full circle
1π = 180o = half a circle π/2 = 90o = ¼ a circle …

8. Example 5

9. Example 6
Calculate the arc length of each bolded arc. Do not round.
A) B)

10. Example 7
Calculate the area of each bolded sector do not round.
A) B)

11. 12-3 Assignments
Primary assignment:
Arc Length & Sector worksheet #1-23 odds
Periods 1, 5, & 7 due Monday 4/23
Periods 2, 4, & 6 due Tuesday 4/24
Work must be shown for full credit
Secondary Assignment:
Arc Length & Sector worksheet #2–24 evens