11 3 areas of circles and sectors
Sponsored Links
This presentation is the property of its rightful owner.
1 / 17

11-3 Areas of Circles and Sectors PowerPoint PPT Presentation


  • 89 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

11-3 Areas of Circles and Sectors

An Image/Link below is provided (as is) to download presentation

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 - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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·r2

A = arear = radius

p. 798


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

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


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

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.


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 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 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

p. 799


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


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


11-3 Assignment

Page 801, 8-22 even


  • Login