Loading in 5 sec....

11-3 Areas of Circles and SectorsPowerPoint Presentation

11-3 Areas of Circles and Sectors

- 96 Views
- Uploaded on
- Presentation posted in: General

11-3 Areas of Circles and Sectors

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

11-3 Areas of Circles and Sectors

You found the circumference of a circle.

- Find areas of circles.

- Find areas of sectors of circles.

The formula for area of a circle is:

A = π·r2

A = arear = radius

p. 798

A = π·r2

A = π·32

A = 9π

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

A = π·r2

49π = π·r2

ππ

49 = r2

r = 7

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.

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.

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

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 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

p. 799

L

125°

12 cm

J

K

Find the area of sector JKL to the nearest tenth.

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

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.

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

Page 801, 8-22 even