Circles: Master the Geometry of Roundness

Question 1

What is the standard form equation of a circle with center (h, k) and radius r?

Accepted Answer

(x - h)^2 + (y - k)^2 = r^2

Answer

(x + h)^2 + (y + k)^2 = r^2

Answer

x^2 + y^2 - 2hx - 2ky + h^2 + k^2 = r^2

Answer

x^2 - 2hx + h^2 + y^2 - 2ky + k^2 = r^2

Question 2

What is the formula to calculate the circumference of a circle?

Accepted Answer

2πr

Answer

πr

Answer

πr²

Answer

2πr²

Question 3

A circle has a radius of 10 cm. What is its area?

Accepted Answer

100π cm²

Answer

10π cm²

Answer

20π cm²

Answer

200π cm²

Question 4

The radius of a circle is 10 cm. What is its diameter?

Accepted Answer

20 cm

Answer

5 cm

Answer

10 cm

Answer

40 cm

Question 5

The diameter of a circle is 20 cm. What is the length of a chord that subtends an angle of 90° at the center?

Accepted Answer

10√2 cm

Answer

10 cm

Answer

20 cm

Answer

20√2 cm

Question 6

What is the area of a circle with a radius of 10 cm?

Accepted Answer

100π cm²

Answer

50π cm²

Answer

150π cm²

Answer

200π cm²

Question 7

A circle has a circumference of 42π cm. What is its diameter?

Accepted Answer

21 cm

Answer

7 cm

Answer

14 cm

Answer

28 cm

Question 8

What is the radius of a circle with a diameter of 10 cm?

Accepted Answer

5 cm

Answer

10 cm

Answer

15 cm

Answer

20 cm

Question 9

A circle has a radius of 7 cm. What is its area?

Accepted Answer

49π cm²

Answer

98π cm²

Answer

147π cm²

Answer

196π cm²

Question 10

If a circle has a radius of 5 cm, what is its diameter?

Accepted Answer

10 cm

Answer

2.5 cm

Answer

5 cm

Answer

25 cm

Question 11

In a circle, the diameter is twice the length of the radius. What is the diameter of a circle with a radius of 10 cm?

Accepted Answer

20 cm

Answer

5 cm

Answer

10 cm

Answer

40 cm

Question 12

Given a circle with radius 5 cm, what is its diameter?

Accepted Answer

10 cm

Answer

2.5 cm

Answer

5 cm

Answer

25 cm

Question 13

Given two circles with radii of 5 cm and 10 cm respectively, what is the ratio of their circumferences?

Accepted Answer

2 : 1

Answer

1 : 2

Answer

1 : 4

Answer

4 : 1

Question 14

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 = 5

Answer

(x - 2)² + (y + 3)² = 5

Answer

(x + 2)² + (y + 3)² = 25

Question 15

Two circles have radii of 5 cm and 8 cm, respectively. What is the ratio of the circumference of the larger circle to that of the smaller circle?

Accepted Answer

8:5

Answer

10:13

Answer

5:8

Answer

13:10

Question 16

A semicircle has a diameter of 14 cm. Calculate its perimeter.

Accepted Answer

21π cm

Answer

49π cm

Answer

35π cm

Answer

14π cm

Question 17

What is the equation of a circle with center (3, 5) and radius 4?

Accepted Answer

(x - 3)² + (y - 5)² = 16

Answer

(x - 3)² + (y + 5)² = 4

Answer

(x + 3)² + (y - 5)² = 16

Answer

(x + 3)² + (y + 5)² = 4

Question 18

Which of the following statements is true about the radii of a circle?

Accepted Answer

All radii are the same length.

Answer

All radii are parallel.

Answer

All radii are perpendicular to each other.

Answer

None of the above.

Question 19

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

Accepted Answer

(60/360)π(10)² cm²

Answer

(120/360)π(10) cm²

Answer

(60/360)π(10) cm²

Answer

(120/360)π(10)² cm²

Question 20

What is the length of the arc of a circle with a radius of 10 cm and a central angle of 120°?

Accepted Answer

(120/360)2π(10) cm

Answer

(60/360)2π(10) cm

Answer

(60/360)π(10) cm

Answer

(120/360)π(10) cm

Question 21

A circular garden has a circumference of 20π meters. What is the radius of the garden?

Accepted Answer

10 meters

Answer

20 meters

Answer

5 meters

Answer

40 meters

Question 22

A chord of a circle is 10 cm long and is 6 cm away from the center of the circle. What is the radius of the circle?

Accepted Answer

8 cm

Answer

5 cm

Answer

12 cm

Answer

10 cm

Question 23

Two circles intersect at two points. What is the relationship between the line segment connecting these points and the centers of the circles?

Accepted Answer

The line segment is the perpendicular bisector of the line segment connecting the centers.

Answer

The line segment is parallel to the line segment connecting the centers.

Answer

The line segment is a chord of one of the circles.

Question 24

What is the area of a circle with a radius of 5 cm? (Use π ≈ 3.14)

Accepted Answer

78.5 cm²

Answer

25 cm²

Answer

157 cm²

Answer

314 cm²

Question 25

A circle has a circumference of 30 cm. What is its radius?

Accepted Answer

5 cm

Answer

15 cm

Answer

10 cm

Answer

2.5 cm

Question 26

Determine the equation of a circle with its center at (2, 3) and a radius of 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 = 25

Answer

(x - 2)² + (y + 3)² = 25

Question 27

Calculate the area of a sector in a circle with a radius of 12 cm and a central angle of 60 degrees.

Accepted Answer

36π cm²

Answer

72π cm²

Answer

144π cm²

Answer

12π cm²

Question 28

A circle has a radius of 5 cm. Determine its circumference. (Use π ≈ 3.14)

Accepted Answer

31.4 cm

Answer

15.7 cm

Answer

78.5 cm

Answer

25 cm

Question 29

A circle has a diameter of 12 cm. Calculate its area. (Use π ≈ 3.14)

Accepted Answer

113.04 cm²

Answer

452.16 cm²

Answer

36 cm²

Answer

37.68 cm²

Question 30

A circular garden has a circumference of 25 meters. Determine the radius of the garden. (Use π ≈ 3.14)

Accepted Answer

3.98 meters

Answer

7.96 meters

Answer

1.27 meters

Answer

12.5 meters

Question 31

A pizza has a diameter of 30 cm. Calculate the area of the pizza. (Use π ≈ 3.14)

Accepted Answer

706.5 cm²

Answer

353.25 cm²

Answer

188.4 cm²

Answer

94.2 cm²

Question 32

Two circles have radii of 4 cm and 6 cm, respectively. Determine the ratio of their circumferences.

Accepted Answer

2:3

Answer

4:9

Answer

1:3

Answer

1:2

Question 33

A circular track has a radius of 50 meters. An athlete runs 4 laps of the track. Calculate the distance covered by the athlete. (Use π ≈ 3.14)

Accepted Answer

1256 meters

Answer

628 meters

Answer

314 meters

Answer

2512 meters

Question 34

A circle is inscribed in a square. The side length of the square is 10 cm. Determine the area of the circle. (Use π ≈ 3.14)

Accepted Answer

78.5 cm²

Answer

157 cm²

Answer

314 cm²

Answer

100 cm²

Question 35

A circular pond has a radius of 7 meters. A path is constructed around the pond, leaving a 2-meter wide space between the pond and the path. Calculate the area of the path.

Accepted Answer

108π m²

Answer

36π m²

Answer

63π m²

Answer

144π m²

Question 36

A sector of a circle has a central angle of 60 degrees. If the radius of the circle is 8 cm, what is the area of the sector?

Accepted Answer

33.51 cm²

Answer

16π cm²

Answer

8π cm²

Question 37

A wheel with a diameter of 70 cm makes 10 revolutions. How far does it travel? (Use π ≈ 3.14)

Accepted Answer

219.8 m

Answer

65.94 m

Answer

21.98 m

Answer

43.96 m