11 3 areas of circles and sectors
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11-3 Areas of Circles and Sectors. You found the circumference of a circle. Find areas of circles. Find areas of sectors of circles. Area of a Circle. The formula for area of a circle is: A = π ·r 2 A = arear = radius. p. 798.

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11-3 Areas of Circles and Sectors

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11 3 areas of circles and sectors

11-3 Areas of Circles and Sectors

You found the circumference of a circle.

  • Find areas of circles.

  • Find areas of sectors of circles.


Area of a circle

Area of a Circle

The formula for area of a circle is:

A = π·r2

A = arear = radius

p. 798


If the radius of c is 3 cm what is its area answer in exact form

If the radius of סּC is 3 cm, what is its area? Answer in exact form.

A = π·r2

A = π·32

A = 9π


11 3 areas of circles and sectors

MANUFACTURING An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.

The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So, the diameter of the cover is 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches.

Area of a circle

Substitution

Use a calculator.

Answer:The area of the cover is about 6082 square inches.


11 3 areas of circles and sectors

A swimming pool company manufactures circular covers for above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover.

A.62.8 ft2

B.254.5 ft2

C.314.2 ft2

D.1256.6 ft2


If the area of c is 49 what is its diameter

If the area of סּC is 49π, what is its diameter?

A = π·r2

49π = π·r2

ππ

49 = r2

r = 7


11 3 areas of circles and sectors

Take the positive squareroot of each side.

= r

ALGEBRAFind the radius of a circle with an area of 58 square inches.

Area of a circle

Substitution

Divide each side by .

4.3 ≈ r

Simplify.

Answer:The radius of the circle is about 4.3 in.


11 3 areas of circles and sectors

ALGEBRA Find the radius of a circle with an area of 45 square inches.

A.3.8 in.

B.4.5 in.

C.5.7 in.

D.7.6 in.


11 3 areas of circles and sectors

The South Rose window in Notre Dame has a diameter of 12.9 meters. Find the area and circumference of the window.

A = π·r2

A = π(12.9)2

A = 166.41π

A = 522.79 meters2

C = 2πr

C = 2π(12.9)

C = 25.8π

C = 81.05 meters


If the area of m is 121 m 2 find its circumference

If the area of סּM is 121 m2, find its circumference.

A = π·r2

121 = π·r2

ππ

38.5 = r2

r = 6.2 m

C = 2πr

C = 2π(6.2)

C = 38.99 m

סּM

What letter is common to both the area and circumference formulas?

r (radius)


Sector area

Sector Area

Sector area is the wedge-shaped interior regions of a circle formed by central angles.


11 3 areas of circles and sectors

A sector of a circle is a region formed by two radii and an arc of circle. ABC is a sector of סּB

A

C

B


Formula for sector length

Formula for Sector Length

p. 799


Is a central angle of k

L

125°

12 cm

J

K

is a central angle of סּK

Find the area of sector JKL to the nearest tenth.

The arc covers 125° out of a total of 360° or


11 3 areas of circles and sectors

PIEA pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth?

Step 1Find the arc measure of a pie slice.

Since the pie is equally divided into 10 slices, each slice will have an arc measure of 360 ÷ 10 or 36.

Step 2Find the radius of the pie. Use this measureto find the area of the sector, or slice.

The diameter is 9 inches, so the radius is 4.5 inches.

Area of a sector

x = 36 and r = 4.5

Use a calculator.

Answer:The area of one slice of pie is about 6.36 square in.


11 3 areas of circles and sectors

PIZZAA pizza has a diameter of 14 inches and is cut into 8 congruent slices. What is the area of one slice to the nearest hundredth?

A.16.21 in2

B.19.24 in2

C.26.43 in2

D.38.48 in2


11 3 assignment

11-3 Assignment

Page 801, 8-22 even


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