1. Do Now Agenda Homework Handout (10 problems)  Do Do Now!
12/5: Use formulas to find circumference & area of circles and use proportions to find arc length & sector area of circles.
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Agenda
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Guided Practice
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Homework
Handout
(10 problems) 

3. We will learn to…
Use formulas to find circumference & area of circles.

4. Circle: Circumference: C = d or C = 2r Area: A = r2 NOTE:
• Distance around the edge of a circle
Formula:
C = d or
C = 2r
Area:
• the size of a surface
Formula:
NOTE:
A = r2
Radius is half the diameter.
-- OR –
Diameter is double the radius.

5. EXAMPLE 1
Use the formula for circumference
Round to the nearest hundredth if necessary.
a. Find the circumference of a circle with a radius of 9 cm
SOLUTION
56.55 cm
ANSWER
C = 2πr
= 2π(9)
= 18π
≈ 56.55

6. EXAMPLE 1
Use the formula for circumference
Round to the nearest hundredth if necessary.
b. Find the radius of a circle with a circumference of 26 m
SOLUTION
4.14 m
ANSWER
C = 2πr =
2πr 26 2π 2π 26 2π = r = r
13/π
4.14 ≈ r

7. Use the formula for area of a circle
EXAMPLE 2
Use the formula for area of a circle
Round to the nearest hundredth if necessary.
a. Find the area of the figure below if its radius is 2.5 cm
SOLUTION
19.63 cm2
ANSWER
A = πr2
= π(2.5)2
= 6.25π
≈ 19.63

8. EXAMPLE 2
Use the formula for area of a circle
Round to the nearest hundredth if necessary.
b. Find the diameter of the CD if its area is cm2.
SOLUTION
d = 12 cm
ANSWER
A = πr2
113.1 = πr2 π π
= r2
113.1 π
= r2 36
6 ≈ r

9. We will learn to…
Use proportions to find arc length & sector area of circles.

10. part of the circumference Sector: Part of area (piece of circle)
Arc:
part of the circumference
Sector:
Part of area (piece of circle)
Arc Length
Arc Length 
Sector Area  = =
Circumference
360°
Area of Circle
360°
Arc Length = (θ/360°) * 2πr
Sector Area = (θ/360°) * πr2

11. Find arc lengths and related measures
EXAMPLE 3
Find arc lengths and related measures
Round to the nearest hundredth if necessary. a.
Find the arc length of AB
SOLUTION
Arc Length
Circumference
360° = 
C = 2(8)
≈ cm x
50.27
360° =
60°
360x =
Arc length ≈ 8.38 cm

12. Find arc lengths and related measures
EXAMPLE 3
Find arc lengths and related measures
Round to the nearest hundredth if necessary.
b. Find the circumference.
SOLUTION
Arc Length
Circumference
360° = 
4.19 C
360°
40° =
40C =
C = in.

13. Find arc lengths and related measures
EXAMPLE 3
Find arc lengths and related measures
Round to the nearest hundredth if necessary.
c. Find the mRTS.
SOLUTION
Arc Length
Circumference
360° = 
C = 2(15.28)
≈ 96 m 44 96 x
360° =
15840 = 96x
mRTS = 165°

14. Find sector areas and related measures
EXAMPLE 4
Find sector areas and related measures
Round to nearest hundredth if necessary. a.
Find the area of small sector
SOLUTION
Sector Area
Area of Circle
360° = 
A = (8)²
≈ units A
201.06
70°
360° =
360A =
A ≈ units2

15. Find sector areas and related measures
EXAMPLE 4
Find sector areas and related measures
Round to nearest hundredth if necessary. b.
Find the area of circle
SOLUTION
Sector Area
Area of Circle
360° =  35 A
360°
40° =
40A = 12600
A = 315 m2

16. You turn  Complete practice problems 1-8 on your handout
First five minutes on your own (in silence)

17. Answers to Practice C ≈ 15.71 in. 5. Area ≈ 615.75 ft.2
diameter ≈ 5.41 ft Area ≈ ft.2
Arc length ≈ 5.89 yd Area ≈ ft.2
C = m Area = cm2

18. part of the circumference Sector: piece of the circle
Arc:
part of the circumference
Sector:
piece of the circle
Arc Length
Arc Length 
Sector Area  = =
Circumference
360°
Area of Circle
360°