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11-3 Areas of Circles and SectorsPowerPoint Presentation

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.

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.

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 above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover.סּC is 49π, what is its diameter?

A = π·r2

49π = π·r2

ππ

49 = r2

r = 7

Take the positive square above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover. root 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.

ALGEBRA above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover. 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.

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 meters. Find the area and circumference of the window.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 meters. Find the area and circumference of the window.

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

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 arc of circle. ABC is a sector of

p. 799

L arc of circle. ABC is a sector of

125°

12 cm

J

K

is a central angle of סּKFind the area of sector JKL to the nearest tenth.

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

PIE arc of circle. ABC is a sector of A 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 1 Find 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 2 Find the radius of the pie. Use this measure to 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.

PIZZA arc of circle. ABC is a sector of A 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 arc of circle. ABC is a sector of

Page 801, 8-22 even

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