6.8 Areas of Circles and Sectors

Theorem 6.20: Area of a CircleThe area of a circle is times the square of the radius.

_____ Ar

2 r

6.8 Areas of Circles and Sectors

Example 1 Use the formula for area of a circleUse the formula for area of a circle

Find the indicated measure.a. Area

Solution

m 2.4

Write formula for area of a circle.2 a. rA

Substitute ____ for r.2.4 2___ 2.4

Simplify. _____ 64.17Use a calculator. m _____ 2 42.55

6.8 Areas of Circles and Sectors

Example 1 Use the formula for area of a circleUse the formula for area of a circle

Find the indicated measure.a. Area b. Diameter

Solution

m 2.42in 201A

Write formula for area of a circle.2 b. rA

Substitute _____ for A.2012 ___ r201Divide each side by ___. _____ 2r98.63Find the positive sq. rt. of each side.r___8

The radius is about ___ inches, so the diameter is about ___ inches8 16

6.8 Areas of Circles and Sectors

Theorem 6.21: Area of a SectorThe ratio of the area of a sector of a circle to the area of the whole circle r2) is equal to the ratio of the measure of the intercepted arc to 360o.

P

A

B

ror ,360

APBsector of Area

2 rABm

____360

APBsector of Area

ABm 2 r

6.8 Areas of Circles and Sectors

Example 2 Find areas of sectorsFind areas of sectors

Find the area of the sector formed by

SolutionStep 1 Find the measure of the minor and major arcs.

RQS. Q

R

S

P o635

and ____ ____, Because mRSRQSm 63 63________360 mRPS 63 297

6.8 Areas of Circles and Sectors

Example 2 Find areas of sectorsFind areas of sectors

Find the area of the sector formed by

Solution

RQS. Q

R

S

P o635

Step 2 Find the areas of the small and large sectors.

2 360

rmRS

Area of small sector =

2__ 360

63 5

_____ 74.13

6.8 Areas of Circles and Sectors

Example 2 Find areas of sectorsFind areas of sectors

Find the area of the sector formed by

Solution

RQS. Q

R

S

P o635

Step 2 Find the areas of the small and large sectors.

2 360

rmRPS

Area of large sector =

2__ 360

297 5

_____ 80.64The areas of the small and large sectors are about _______ square units and _______ square units, respectively.

74.1380.64

6.8 Areas of Circles and Sectors

Example 3 Use the Area of a Sector TheoremUse the Area of a Sector Theorem

Use the diagram to find the area of

Solution

C

A

B

452m 22A .C.

of Area360

mABArea of sector ACB = .C.

of Area360

____

4522 C.

of Area____ .C.176

The area of is ______ square meters.C. 176

6.8 Areas of Circles and SectorsCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.

1. Find the radius of the circle.

2ft 154A 2 rA 2 154 r

2r 02.49r 7 ft

6.8 Areas of Circles and SectorsCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.

2. Find the areas of the sectors formed by RQS. P

R

S

Q 106

ft 92

360r

mRS

Area of small sector =

2 360

106

9 93.74 2ft

2 360

rmRPS

Area of large sector =

2 360

254

9 54.179 2ft

6.8 Areas of Circles and SectorsCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.

3. Find the area of G..

F

H

G2yd 6.4A 08

of Area360

mFHArea of sector FGH = G.

of Area360

80

4.6 G.

of Area G.8.28

8.28 2yd

6.7 Circumference and Arc Length

Pg. 242, 6.8 #1-22