Geometry: Circles - Master the Properties and Applications of Circles

Question 1

A farmer has a circular plot of land with a radius of 50 meters. How many meters of fencing does he need to enclose the entire plot?

Accepted Answer

100π meters

Answer

50π meters

Answer

250π meters

Answer

100 meters

Question 2

Find the area of a circular flower bed with a radius of 5 centimeters.

Accepted Answer

25π cm²

Answer

10π cm²

Answer

50π cm²

Answer

100π cm²

Question 3

In a circle with radius 'r', an angle at the center intercepts an arc of length 'a'. What is the measure of the angle?

Accepted Answer

a/r

Answer

r/a

Answer

a^2/r^2

Answer

r^2/a^2

Question 4

Which formula calculates the circumference, C, of a circle using its radius, r?

Accepted Answer

C = 2πr

Answer

C = πr

Answer

C = πr^2

Answer

C = 4πr

Question 5

To re-landscape a circular garden with a radius of 5 meters, which formula should be used to calculate the area that needs to be re-landscaped?

Accepted Answer

Area = πr²

Answer

Area = 2πr

Answer

Area = πd

Answer

Area = 2πd²

Question 6

Which of the following is the correct formula for the diameter of a circle?

Accepted Answer

d = 2r

Answer

d = r

Answer

d = r²

Question 7

In a circle, what is the relationship between the diameter (d) and the radius (r)?

Accepted Answer

d = 2 * r

Answer

d = r / 2

Answer

d = 3 * r

Answer

d = 4 * r

Question 8

In a circle, the radius is half the length of the diameter. What's the ratio of the radius to the diameter?

Accepted Answer

1:2

Answer

2:1

Answer

1:3

Answer

3:1

Question 9

To calculate the area of a circle, which formula should you use?

Accepted Answer

A = πr^2

Answer

A = πr

Answer

A = 2πr

Question 10

What is the ratio of the circumference to the diameter of a circle?

Accepted Answer

π : 2

Answer

2 : π

Answer

π : 4

Answer

4 : π

Question 11

The area of a circle is 36π square units. What is its circumference?

Accepted Answer

12π units

Answer

6π units

Question 12

In a circle, how are a tangent line and a radius drawn to the point of tangency related?

Accepted Answer

They form a right angle.

Answer

They form an acute angle.

Answer

They form an obtuse angle.

Answer

They are parallel.

Question 13

Which formula calculates the area of a circle?

Accepted Answer

A = πr^2

Answer

A = 2πr

Answer

A = 4πr

Answer

A = 2πr^2

Question 14

Which equation gives the circumference (C) of a circle in terms of its diameter (d)?

Accepted Answer

C = πd

Answer

C = πr^2

Answer

r = πd/2

Answer

d = 2πr

Question 15

A circle has a circumference of 12π centimeters. What's its radius?

Accepted Answer

6 centimeters

Answer

12 centimeters

Answer

18 centimeters

Answer

24 centimeters

Question 16

Find the diameter of a circle with a radius of 5 centimeters.

Accepted Answer

10 centimeters

Answer

25 centimeters

Answer

5 centimeters

Question 17

In a circle, two chords intersect at point P, dividing each other into two segments. What is the relationship between the products of the lengths of the segments formed by the intersection?

Accepted Answer

The products of the segments formed by the intersection are equal.

Answer

The sum of the products is equal to the length of the shorter chord.

Answer

The difference between the products is equal to the length of the longer chord.

Answer

The ratio of the products is equal to the ratio of the lengths of the chords.

Question 18

Which of the following equations represents the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πd

Answer

A = πr²

Answer

C = πr

Question 19

Determine the area of a sector with a central angle of 90° and a radius of 5 cm.

Accepted Answer

12.5π cm²

Answer

25π cm²

Answer

50π cm²

Answer

100π cm²

Question 20

When two chords of a circle intersect inside the circle, what remains constant?

Accepted Answer

The product of their lengths

Answer

The sum of their lengths

Answer

Their perpendicular bisectors

Answer

The area of the circle

Question 21

Determine the radius of the circle inscribed in a square with a side length of 10 cm.

Accepted Answer

5 cm

Answer

2.5 cm

Answer

7.5 cm

Answer

10 cm

Question 22

What property is exclusive to circles, setting them apart from all other polygons?

Accepted Answer

Equal radii from the center to any point on the circumference

Answer

Equal side lengths

Answer

Congruent angles

Answer

Parallel sides

Question 23

What is the circumference of a circle with a radius of 5 cm? (Round your answer to the nearest tenth)

Accepted Answer

15.7 cm

Answer

10π cm

Answer

25π cm

Answer

50π cm

Question 24

A sector of a circle has a central angle of 60° and a radius of 10 cm. What is the area of the sector? (Round your answer to the nearest tenth)

Accepted Answer

17.28 cm²

Answer

10π cm²

Answer

30π cm²

Answer

60π cm²

Question 25

A circle is inscribed in a square with a side length of 8 cm. What is the radius of the circle?

Accepted Answer

4 cm

Answer

2 cm

Answer

6 cm

Answer

8 cm

Question 26

Which of the following equations represents the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πr

Answer

C = πr²

Answer

C = 2πr²

Question 27

To find the area of a circle, which formula should you use?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = 4πr

Answer

A = π²r

Question 28

If a circle has a radius of 5 centimeters, what is its circumference?

Accepted Answer

10π centimeters

Answer

5π centimeters

Answer

25π centimeters

Answer

50π centimeters

Question 29

Which of the following is the formula for calculating the circumference of a circle?

Accepted Answer

2πr

Answer

πr²

Answer

πd

Answer

4πr

Question 30

Calculate the area of a circle with a radius of 5 cm.

Accepted Answer

25π cm²

Answer

100π cm²

Answer

15π cm²

Answer

50π cm²

Question 31

Which property describes the relationship between chords and the center of a circle?

Accepted Answer

All chords are equidistant from the center.

Answer

All tangents are parallel.

Answer

The diameter is always longer than the radius.

Answer

The circumference is always greater than the area.

Question 32

Determine the radius of a circle with a circumference of 20π cm.

Accepted Answer

10 cm

Answer

15 cm

Answer

5 cm

Answer

20 cm

Question 33

Find the area of a sector in a circle with a radius of 10 cm and a central angle of 60 degrees.

Accepted Answer

25π cm²

Answer

50π cm²

Answer

100π cm²

Answer

10π cm²

Question 34

Which of the following is the definition of a tangent to a circle?

Accepted Answer

A line that intersects the circle at exactly one point

Answer

A line that passes through the circle's center

Answer

A line that intersects the circle at two points

Answer

A line that is parallel to the circle

Question 35

A circle has a radius of 7 centimeters. What is its area? (Use π ≈ 3.14)

Accepted Answer

153.86 cm²

Answer

153.94 cm²

Answer

21.98 cm²

Answer

43.96 cm²

Question 36

A circular garden has a circumference of 25 meters. What is its diameter? (Use π ≈ 3.14)

Accepted Answer

7.96 meters

Answer

3.98 meters

Answer

15.92 meters

Answer

12.5 meters

Question 37

A circular pizza has a diameter of 12 inches. What is its area? (Use π ≈ 3.14)

Accepted Answer

113.04 inches²

Answer

75.4 inches²

Answer

37.7 inches²

Answer

452.4 inches²

Question 38

A circular track has a radius of 50 meters. If an athlete runs 4 laps around the track, what is the total distance covered? (Use π ≈ 3.14)

Accepted Answer

1256 meters

Answer

628 meters

Answer

314 meters

Answer

2512 meters

Question 39

A circular garden has an area of 153.86 square meters. What is the radius of the garden? (Use π ≈ 3.14)

Accepted Answer

7 meters

Answer

14 meters

Answer

28 meters

Answer

3.5 meters

Question 40

A circle has a circumference of 25π inches. What is the radius of the circle?

Accepted Answer

12.5 inches

Answer

6.25 inches

Answer

25 inches

Answer

50 inches

Question 41

A circular mirror has a radius of 8 inches. What is the area of the mirror?

Accepted Answer

64π square inches

Answer

32π square inches

Answer

16π square inches

Answer

128π square inches

Question 42

A circular park has a diameter of 50 meters. What is the circumference of the park?

Accepted Answer

50π meters

Answer

2500π meters

Answer

100π meters

Answer

25π meters

Question 43

What is the circumference of a circle with a radius of 5 cm?

Accepted Answer

10π cm

Answer

50π cm

Answer

25π cm

Answer

5π cm

Question 44

What is the area of a circle with a diameter of 10 units?

Accepted Answer

25π sq. units

Answer

100π sq. units

Answer

10π sq. units

Answer

50π sq. units

Question 45

A circle has a circumference of 20π cm. What is its radius?

Accepted Answer

10 cm

Answer

5 cm

Answer

20 cm

Answer

15 cm

Question 46

What is the equation of a circle with center (2, -3) and radius 5?

Accepted Answer

(x - 2)^2 + (y + 3)^2 = 25

Answer

(x + 2)^2 + (y - 3)^2 = 25

Answer

(x + 2)^2 + (y + 3)^2 = 5

Answer

(x - 2)^2 + (y - 3)^2 = 5

Question 47

A circle has an area of 49π sq. units. What is its diameter?

Accepted Answer

14 units

Answer

7 units

Answer

21 units

Answer

28 units

Question 48

What is the length of the tangent from an external point (6, 8) to a circle with center (2, 2) and radius 5?

Accepted Answer

6

Answer

12

Answer

10

Answer

8

Question 49

Two circles have radii of 6 cm and 8 cm, respectively. What is the radius of the circle inscribed in the larger circle and tangent to the smaller circle?

Accepted Answer

2 cm

Answer

4 cm

Answer

8 cm

Answer

6 cm

Question 50

What is the area of the sector of a circle with radius 10 cm and central angle of 60 degrees?

Accepted Answer

25π sq. cm

Answer

100π sq. cm

Answer

50π sq. cm

Answer

75π sq. cm