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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. - PowerPoint PPT Presentation
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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·r2
A = area r = radius
p. 798
If the radius of ּסC 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.
Answer: The area of the cover is about 6082 square inches.
Area of a circle
Substitution
Use a calculator.
A. 62.8 ft2
B. 254.5 ft2
C. 314.2 ft2
D. 1256.6 ft2
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.
If the area of ּסC is 49π, what is its diameter?
A = π·r2
49π = π·r2
π π
49 = r2
r = 7
ALGEBRA Find the radius of a circle with an area of 58 square inches.
Answer: The radius of the circle is about 4.3 in.
Area of a circle
Substitution
Divide each side by .
Simplify.4.3 ≈ r
Take the positive squareroot of each side.= r
A. 3.8 in.
B. 4.5 in.
C. 5.7 in.
D. 7.6 in.
ALGEBRA Find the radius of a circle with an area of 45 square inches.
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 ּסM is 121 m2, find its circumference.
A = π·r2
121 = π·r2
π π
38.5 = r2
r = 6.2 m
C = 2πr
C = 2π(6.2)
C = 38.99 m
Mּס
What letter is common to both the area and circumference formulas?
r (radius)
Sector AreaSector 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 ּסB
A
BC
Formula for Sector Length
360
degreesarcA 2 r
p. 799
is a central angle of ּסK
The arc covers 125° out of a total of 360° or
JK
L
125° 12 cm
2A r
360
125
Find the area of sector JKL to the nearest tenth.
JKL
1.157360
12512A 2
PIE 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 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.
A. 16.21 in2
B. 19.24 in2
C. 26.43 in2
D. 38.48 in2
PIZZA 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?
11-3 Assignment
Page 801, 8-22 even