Warm up for Section 4.8

Answers to Warm up for Section 4.8

C = 2(8)C = 16C ≈ 50.27 ft

65.98 = 2r65.98/(2) = r 10.50 cm ≈ rLength AB

= 150 360≈ 47.12 in.

∙ 2(18)

1. 2.

3. 4.

5. 6.

7. 8. 114.02°

9. 58.03 in. 10. 20.53 cm

11. 30 + 5π ≈ 45.71 mm

4.7 Homework Answers

216.68 m

39

12.41 cm

15 47.12 in. 54 169.66 ft

2 6.28 cm 15 47.12 in.

77.33 ft

3

Section 4.8

Area of a Circle and a Sector

Standard: MM2G3 cd

Essential Question: How do I find the area of a sector using the measure of a central angle?

Before beginning this section, you must remember a few formulas that you have learned in the past:

The area of a circle is given by the formula:

2rA

A sector is the region bounded by two radii of the circle and their intercepted arc. It is a portion of the entire area.

A is the center of the circle at right.

What is the total area of the circle?

2(6) 113.10A

We will use this information to find the area of theshaded sector. The formula for the area of a sector is very similar to the formula for arc length.

A

6

40˚

Using the formula above, we can determine the area of the shaded sector.

The formula for the area of a sector is given by:

A

6

40˚36360

40 a

1440

360a

360 1440a

Area of Sector Arc Measure

Area of Circle 360

4 12.57a

Find the area of circle Y.

X

Y

Z

Area of shadedSector = 95 cm2 A

95

360

150

228150

)95(360A

A150)95(360

The area of the circle is 228 cm2.

150˚

Area of circle = A

A

B

C

21 mm

441360

110 a

33.423360

)441(110

a

)441(110360 a

Area of circle = 441212

Area small sector:

Area large sector:

11.96233.423441

Find the area of both sectors.

110˚

A

B

C

21 mm

The small sector has area 423.33 mm2 and the large sector has area 962.11 mm2.

110˚

F

H

G

Area of shaded region is 123.45 m2

A

45.123

360

70

44442634.89

70A

70 44442A

Area of circle = A

Find the area of circle H.

The area of circle H is 634.89 m2.

70˚