11.3: Areas of Circles and Sectors
Name:______________________ Period:_______
Warm-Up: Use Circle D to answer the following questions.
1. Name a diameter.
2. If NL = 3 in, find the circumference.
3. Find m ̂ .
4. Find the length of ̂ if DM= 5 feet.
What is the formula for the area of a circle?
A=
Example 1: Find the area of a circle with a radius
of 10 cm to the nearest tenth.
Example 2: Find the area of a circle with a
diameter of 12 m to the nearest tenth.
Example 3: What is the radius to the nearest tenth
of a circle with an area of 48 ft2?
Example 4: Find the diameter to the nearest tenth
of a circle with an area of 6400 cm2.
.
Suppose you have a pizza that is cut into 8 slices and the pizza has a radius of 8
inches.
How much pizza did you eat?
If you only ate 4 slices, how much pizza did you eat?
If you only ate 1 slice, how much pizza did you eat?
 A ____________________ is a region of a circle bounded by a central angle and
its intercepted major or minor arc. A slice of pizza is an example of a sector of a
circle. The formula for the area of a sector is similar to the formulas for arc length.
Area of a Sector Formula:
Example 5: 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 tenth?
Example 7: If the area of sector is 34 m2 and the
radius is 6m, find the central angle to the nearest
degree.
Example 6: L and M are 2 points on circle R with
radius 50cm and m∠LRM = 150°. Find the areas of
the sectors formed by m∠LRM to the nearest cm2.
Example 8: What is the radius of a circle to a tenth
of a foot when a 50° sector has an area of 120 ft2?
Example 9: Find the orange region’s area to the nearest tenth.
Example 10:
Which figure has the most orange area?
Example 11: Find the area of the shaded region below.
Example 12: A windshield wiper blade is 18 inches long. To the nearest square inch, what is the area covered
by the blade as it rotates through an angle of 122°?
Example 13: A bicycle chain is shown at the left,which travels around the
front and rear sprocket. The circumference of each sprocket is shown.
What is the length of the chain?
11.3 Homework
Find the area of each circle. Round to the nearest tenth.
1.
2.
3.
Find the indicated measure. Round to the nearest tenth.
4. The area of a circle is 3.14 square centimeters. Find the diameter.
5. Find the diameter of a circle with an area of 855.3 square millimeters.
6. The area of a circle is 201.1 square inches. Find the radius.
7. Find the radius of a circle with an area of 2290.2 square feet.
Find the area of each shaded sector. Round to the nearest tenth.
8.
9.
10.
11. Sadie wants to draw a clock face on a circular piece of cardboard. If the clock face has a diameter of 20 centimeters
and is divided into congruent pieces so that each sector is 30°, what is the area of each piece?
12. Julie needs to cover the top and bottom of a can of soup with construction paper to include in her art project. Each
circle has a diameter of 7.5 centimeters. What is the total area of the can that Julie must cover?