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Perimeter and Area of Circles and Sectors (9-2 and 11-3)

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Perimeter and Area of Circles and Sectors (9-2 and 11-3)

I CAN

- Find the circumference and area of a circle
- Find the arc length of a sector
- Find the area of a sector

Find the unknown side lengths in each special right triangle.

1. a 30°-60°-90° triangle with hypotenuse 2 ft

2. a 45°-45°-90° triangle with leg length 4 in.

3. a 30°-60°-90° triangle with longer leg length 3m

is defined as the ratio of

the circumference C to

the diameter d, or

A circleis the locus of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol and its center. Ahas radius r= ABand diameter d= CD.

Solving for C gives the formula

C = d. Also d = 2r, so C = 2r.

Arc length is related to the circumference of a circle.

It is a fraction of the circumference of the circle

One way of finding arc length.

Fold a sheet of notebook paper in half.

You will be writing examples for circumference

and arc length on the left half of the paper.

Complete each of the examples on the

following slides on your “foldable” notes.

Draw and label your pictures correctly.

Finding circumference and arc lengths

I. Find the circumference ofP, “circle with center P.”

C = 2r

P

●

24 cm

C = d

C = 24 cm

Finding circumference and arc lengths

II. Find the arc length (L) of AB

●A

“piece of the circumference”

●B

P

●

24 cm

You can use proportions to easily find the arc length.

Part 90 = L

Whole 360 24

Remember the circumference is 24

1 = L

4 24

4L = 24

Cross multiply to solve proportion

L = 6 cm

Don’t forget units!

Finding circumference and arc lengths

III. Find the arc length (L) of AB

●A

“piece of the circumference”

●B

80º

P

●

24 cm

Part 80 = L

Whole 360 24

L = 16 cm

3

Don’t forget units!

Just likearc lengthis related to thecircumferenceof a circle,

the area of a sector is related to the area of the circle.

The area of a sector is a fraction of the area of the circle

of a sector

Refer back to your foldable notes.

You will be writing examples for area of

circle and area of sectors on the right

half of the paper.

Complete each of the examples on the

following slides on your “foldable” notes.

Draw and label your pictures correctly.

Finding area of circles and area of sectors

I. Find the area of P

A = r2

24 c m

●

P

A = (12)2

A = 144 cm2

Don’t forget your units!

Finding area of circles and area of sectors

II. Find the sector area (S) of sector APB

●A

“piece of the area”

●B

P

●

24 cm

You can use proportions to easily find the sector area

Part 90 = S

Whole 360 144

Remember the total area is 144

1 = S

4 144

4S = 144

Cross multiply to solve proportion

S = 36 cm2

Don’t forget units!

Finding the area of circles and area of sectors

III. Find the sector area (S) of sector APB

●A

“piece of the area”

●B

80º

P

●

24 cm

Part 80 = S

Whole 360 144

S = 32 cm2

Don’t forget units!

A segment of a circle is a region bounded by

an arc and its chord.

Find each arc length. Give answers in terms of and rounded to the nearest hundredth.

FG

5.96 cm 18.71 cm

ON YOUR OWN

Find each arc length. Give your answer in terms of and rounded to the nearest hundredth.

GH

Find the area of each sector. Give answers in terms of and rounded to the nearest hundredth.

sector HGJ

= 52.4 m2 164.62 m2

Find the area of each sector. Give your answer in terms of and rounded to the nearest hundredth.

sector ACB

= 0.25 m2 0.79 m2

Find each measure. Give answers in terms of and rounded to the nearest hundredth.

1. area of sector LQM

7.5in223.56 in2

2. length of NP

2.5 in. 7.85 in.

3. The gear of a grandfather clock has a radius of 3 in. To the nearest tenth of an inch, what distance does the gear cover when it rotates through an angle of 88°?

4.6 in.

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