Transcript Areas of Circles and Sectors LESSON 10-7 Additional Examples A circular archery target has a 2-ft diameter.

Areas of Circles and Sectors
LESSON 10-7
Additional Examples
A circular archery target has a 2-ft diameter. It is
yellow except for a red bull’s-eye at the center with a 6-in.
diameter. Find the area of the yellow region. Round your
answer to the nearest whole number.
Find the areas of the archery target and the bull’s-eye.
The radius of the archery target is
2
= 1 ft.
2
Because the diameters are in different units, convert 1 ft to 12 in.
The radius of the archery target is 1 ft = 12 in.
The area of the archery target is
HELP
r2 =
(12)2 = 144
in.2
GEOMETRY
Areas of Circles and Sectors
LESSON 10-7
Additional Examples
(continued)
The radius of the red region is
The area of the red region is
6
= 3 in.
2
r2 =
(3)2 = 9
in.2
area of archery target – area of red region = area of yellow region
144
–
9
=
135
Use a calculator. 135
The area of the yellow region is about 424 in.2
HELP
Quick Check
GEOMETRY
Areas of Circles and Sectors
LESSON 10-7
Additional Examples
.
. of .
Find
the area of sector ACB. Leave your answer in terms
mAB
area of sector ACB = 360 •
=
100
360
•
r2
(6)2
= 5 • 36
18
= 10
The area of sector ACB is 10
m2.
Quick Check
HELP
GEOMETRY
Areas of Circles and Sectors
LESSON 10-7
Additional Examples
Find the area of the shaded segment. Round your answer to
the nearest tenth.
Step 1: Find the area of sector AOB.
area of sector AOB = mAB •
360
r2
Use the formula for
area of a sector.
120
= 360 •
= 1 • 576
3
HELP
(24)2
= 192
Substitute.
Simplify.
GEOMETRY
Areas of Circles and Sectors
LESSON 10-7
Additional Examples
(continued)
Step 2: Find the area of AOB.
You can use a 30°-60°-90° triangle to find the height h of
24 = 2h
hypotenuse = 2 • shorter leg
12 = h
AB = 3 • 12 = 12
2
AB = 24 3
Divide each side by 2.
AOB has base 12
1
A = bh
2
A = 1 (24 3 )(12)
2
A = 144 3
HELP
3
longer leg =
AOB and AB.
3 • shorter leg
Multiply each side by 2.
3 ft + 12
3 ft, or 24
3 ft and height 12 ft.
Area of a triangle
Substitute 24 for b and 12 for h.
Simplify.
GEOMETRY
Areas of Circles and Sectors
LESSON 10-7
Additional Examples
(continued)
Step 3: Subtract the area of AOB from the area of sector AOB
to find the area of the segment of the circle.
area of segment = 192
– 144
3
Use a calculator.
To the nearest tenth, the area of the shaded segment is 353.8 ft2.
Quick Check
HELP
GEOMETRY