AnswersCR CCSS Math 2 S2 M2960OXArea of a Circle and a Sector

Area of a Circle and a Sector Answers

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Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded.

Question illustration
A
4
Option A
B
8
Option B
C
16
Option C
D
20
Option D
2
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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
3

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
4

The measure of central angle XYZ is 1.25 radians.

Question illustration
A
10 units2
Option A
B
20 units2
Option B
C
40 units2
Option C
D
80 units2
Option D
5

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
6

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
7

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.
8

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
9

The circular face of a watch has an area that measures between 800 and 900 square millimeters.What could be the radius of the watch face? Use 3.14 for .

Question illustration
A
14 mm
B
15 mm
C
16 mm
D
17 mm
10

Circles C and D overlap. The distance from point C to point D is 7 centimeters.

Question illustration
A
7
Option A
B
14
Option B
C
49
Option C
D
98
Option D
11

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
12

Circles C and D overlap. The distance from point C to point D is 7 centimeters.

Question illustration
A
7
Option A
B
14
Option B
C
49
Option C
D
98
Option D
13

2 smaller circles are within a larger circle. The smallest circle has radius D C. Line segment C B is the distance to the rim of the next circle. Line segment B A is the distance to the rim to the next circle.

Question illustration
A
80
Option A
B
96
Option B
C
208
Option C
D
464
Option D
14

Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded.

Question illustration
A
4
Option A
B
8
Option B
C
16
Option C
D
20
Option D
15

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
16

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
17

Circles G and X are connected at point H. The length of G H is 6 centimeters and the length of H X is 8 centimeters.

Question illustration
A
16
Option A
B
36
Option B
C
49
Option C
D
98
Option D
18

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
19

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
20

three

Question illustration
T
The ratio of the measure of central angle PQR to the measure of the entire circle is .
Option T
T
The area of the shaded sector is 4 units2.
T
The area of the shaded sector depends on the length of the radius.
T
The area of the shaded sector depends on the area of the circle.
T
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.

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