AnswersPA-Geometry B-CRInscribed Angles

Area of a Circle and a Sector Answers

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In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula .

Question illustration
A
The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
B
The central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.
C
The central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.
D
The central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.
2
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The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram.

Question illustration
A
A = (2πr)(r)
B
A = (2πr)(2r)
C
A =(2πr)(r)
Option C
D
A =(2πr)(r2)
Option D
3

Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona’s circle?

A
7
Option A
B
14
Option B
C
28
Option C
D
49
Option D
4

Circle G is shown. Line segment F G is a radius with length 3.

Question illustration
A
6
Option A
B
9
Option B
C
12
Option C
D
18
Option D
5

Circle L is shown. Line segments K L and M L are radii. The length of K L is 9. Angle M L K is 120 degrees. Sector M L K with a 120 degree angle is shaded.

Question illustration
A
9
Option A
B
27
Option B
C
81
Option C
D
162
Option D
6

Which statements are true about circle Q? Select three options.

A
The ratio of the measure of central angle PQR to the measure of the entire circle is .
Option A
B
The area of the shaded sector is 4 units2.
C
The area of the shaded sector depends on the length of the radius.
D
The area of the shaded sector depends on the area of the circle.
E
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.
7

Circle X and Y are connected at one side. Larger circle C surrounds both circles. Line segment W Z is the diameter of circle C. The line segment goes through all points of the other circles. The length of W X is 8 and the length of Y Z is 10.

Question illustration
A
81
Option A
B
164
Option B
C
324
Option C
D
1296
Option D
8

Circle V is shown. Line segment T V is a radius with length 14 feet.

Question illustration
A
14
Option A
B
28
Option B
C
49
Option C
D
196
Option D
9

The measure of central angle YCZ is 80 degrees.

Question illustration
A
18 units2
Option A
B
36 units2
Option B
C
45 units2
Option C
D
81 units2
Option D
10

Smaller circle C is inside larger circle C. The smaller circle is labeled the garden. The radius of the smaller circle is 8 feet. The distance from the rim of the inner circle to the rim of the outer circle is 3 feet.

Question illustration
A
172.70 ft2
B
178.98 ft2
C
200.96 ft2
D
379.94 ft2

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