Circles: Learn about the Geometry of Circles with Interactive Quizzes

Question 1

Which formula calculates the area of a circle with radius 'r'?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πd

Answer

A = r²

Question 2

What is the area of a circle with a radius of 3 cm?

Accepted Answer

9π cm²

Answer

18π cm²

Answer

27π cm²

Answer

36π cm²

Question 3

Which of the following is NOT a characteristic of a circle?

Accepted Answer

It is a regular polygon.

Answer

The radius is constant.

Answer

It contains a single center point.

Answer

Its circumference exceeds its diameter.

Question 4

If a circle's diameter is 10 cm, what is its radius?

Accepted Answer

5 cm

Answer

2.5 cm

Answer

10 cm

Answer

20 cm

Question 5

A circle has an area of 25π cm². What is its diameter?

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 6

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

Accepted Answer

25π cm²

Answer

50π cm²

Answer

75π cm²

Answer

100π cm²

Question 7

Which of the following is not a property of a circle?

Accepted Answer

Equal perimeters

Answer

Equal radii

Answer

Equal angles

Answer

Equal chords

Question 8

Find the circumference of a semicircle with a radius of 7 cm.

Accepted Answer

14π cm

Answer

7π cm

Answer

21π cm

Answer

28π cm

Question 9

Which of the following is NOT a property of a circle?

Accepted Answer

Equal side lengths

Answer

Constant radius

Answer

Fixed center

Answer

Smooth circumference

Question 10

The distance from the center of a circle to any point on its edge is called the:

Accepted Answer

Radius

Answer

Diameter

Answer

Chord

Answer

Tangent

Question 11

The formula for calculating the circumference of a circle with radius 'r' is:

Accepted Answer

2πr

Answer

πr

Answer

πr²

Answer

4πr²

Question 12

A sector is a portion of a circle bounded by two radii and an:

Accepted Answer

Arc

Answer

Chord

Answer

Tangent

Answer

Diameter

Question 13

The area of a circle with radius 'r' is:

Accepted Answer

πr²

Answer

πr

Answer

2πr

Answer

4πr²

Question 14

Which of the following shapes is NOT similar to a circle?

Accepted Answer

Square

Answer

Ellipse

Answer

Oval

Answer

Sphere

Question 15

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

Accepted Answer

10 cm

Answer

2.5 cm

Answer

5 cm

Answer

15 cm

Question 16

A circle has a circumference of 6π cm. What is its radius?

Accepted Answer

3 cm

Answer

1 cm

Answer

2 cm

Answer

6 cm

Question 17

Which of the following is NOT a property of a circle?

Accepted Answer

Area proportional to the square of the circumference

Answer

Constant radius

Answer

Symmetry

Answer

Diameter equals twice the radius

Question 18

Which of the following is the correct formula for the radius (r) of a circle, given its circumference (C)?

Accepted Answer

r = C / 2π

Answer

r = 2π / C

Answer

r = π / C

Answer

r = 2C / π

Question 19

Which of the following is the correct formula for the area (A) of a circle, given its radius (r)?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πr

Answer

A = 2r²

Question 20

Which of the following is NOT a characteristic of a circle?

Accepted Answer

Its circumference is always greater than its area.

Answer

It has a single center point.

Answer

It has a constant radius.

Answer

All points on its circumference are equidistant from the center.

Question 21

Determine the diameter of a circle with a circumference of 20π centimeters:

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 22

What is the equation of a circle with center at the point (2, 3) and a radius of 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 = 25

Answer

(x + 2)² + (y + 3)² = 5

Question 23

Find the length of the arc of a circle with a radius of 15 cm and a central angle of 90°:

Accepted Answer

22.5 cm

Answer

7.5 cm

Answer

15 cm

Answer

30 cm

Question 24

Which property is NOT associated with a circle?

Accepted Answer

Perimeter

Answer

Radius

Answer

Circumference

Answer

Diameter

Question 25

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

Accepted Answer

10π cm

Answer

25π cm

Answer

5π cm

Answer

10 cm

Question 26

What's the area of a circle with a diameter of 12 cm?

Accepted Answer

36π cm²

Answer

144π cm²

Answer

12π cm²

Answer

72π cm²

Question 27

Find the equation of the circle with center (2, 3) and radius 4:

Accepted Answer

(x-2)²+(y-3)²=4

Answer

(x-3)²+(y-2)²=16

Answer

(x+2)²+(y+3)²=4

Answer

(x+3)²+(y+2)²=16

Question 28

A circle is inscribed within a square with a side length of 10 cm. What is the radius of the circle?

Accepted Answer

5√2 cm

Answer

5 cm

Answer

2.5 cm

Answer

2.5√2 cm

Question 29

Two circles are tangent externally. The radii of the circles are 3 cm and 4 cm. What is the length of the common external tangent?

Accepted Answer

7 cm

Answer

1 cm

Answer

5 cm

Answer

9 cm

Question 30

In a cyclic quadrilateral, what is the relationship between the opposite angles?

Accepted Answer

Supplementary (add up to 180 degrees)

Answer

Complementary (add up to 90 degrees)

Answer

Adjacent (share a side)

Question 31

Which formula represents the area of a circle?

Accepted Answer

πr²

Answer

2πr

Answer

4πr

Answer

r²

Question 32

Which of the following is NOT a property of circles?

Accepted Answer

All circles have the same area.

Answer

The radius of a circle is always less than the diameter.

Answer

Circles have 360 degrees.

Answer

Circles are symmetrical.

Question 33

Which of the following is a chord of a circle?

Accepted Answer

A line segment that connects two points on the circle.

Answer

A line that passes through the center of the circle.

Answer

A line that intersects the circle at one point.

Question 34

What is the formula for the circumference of a circle with radius 'r'?

Accepted Answer

2πr

Answer

4πr²

Answer

πr²

Answer

πd

Question 35

Which of the following is not a property of a circle?

Accepted Answer

It has four sides.

Answer

It can be inscribed in a square.

Answer

It has a constant radius.

Answer

It is a closed figure.

Question 36

Find the radius of a circle with a diameter of 10 cm.

Accepted Answer

5 cm

Answer

2.5 cm

Answer

10 cm

Answer

20 cm

Question 37

Which of the following formulas represents the area of a circle?

Accepted Answer

πr²

Answer

2πr

Answer

πd

Answer

πr

Question 38

Given a circle with a radius of 5 centimeters, determine its circumference.

Accepted Answer

10π cm

Answer

25π cm

Answer

5π cm

Answer

50π cm

Question 39

Determine the measure of an inscribed angle that intercepts an arc of 120 degrees.

Accepted Answer

60°

Answer

30°

Answer

120°

Answer

90°

Question 40

Which theorem establishes a relationship between the lengths of tangents drawn from an external point to a circle?

Accepted Answer

Tangent-Tangent Theorem

Answer

Angle Bisector Theorem

Answer

Circle Inscribed Angle Theorem

Answer

Pythagorean Theorem

Question 41

What is the radius of a circle with a circumference of 2π cm?

Accepted Answer

1 cm

Answer

2 cm

Answer

4 cm

Answer

π cm

Question 42

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

Accepted Answer

25π cm²

Answer

50π cm²

Answer

10π cm²

Answer

5π cm²

Question 43

Which of these is NOT a theorem related to circles?

Accepted Answer

The Pythagorean theorem

Answer

The angle inscribed in a semicircle is a right angle.

Answer

Tangents to a circle from an external point are equal in length.

Answer

The area of a circle is proportional to the square of its radius.

Question 44

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 45

A circular garden has a diameter of 10 meters. What is its area?

Accepted Answer

78.5 square meters

Answer

314 square meters

Answer

100 square meters

Answer

31.4 square meters

Question 46

Which of these is NOT a property of a circle?

Accepted Answer

All points on the circle are equidistant from a single point inside the circle.

Answer

The circumference of a circle is directly proportional to its diameter.

Answer

A circle has a constant curvature.

Question 47

A pizza has a radius of 12 inches. What is its area?

Accepted Answer

452.4 square inches

Answer

37.7 square inches

Answer

150.7 square inches

Answer

144 square inches

Question 48

A circular track has a circumference of 400 meters. What is the diameter of the track?

Accepted Answer

127.3 meters

Answer

200 meters

Answer

63.7 meters

Answer

400 meters

Question 49

A circular pool has a diameter of 15 feet. What is the circumference of the pool?

Accepted Answer

47.1 feet

Answer

70.7 feet

Answer

23.6 feet

Answer

15 feet

Question 50

The ratio of a circle's circumference to its diameter is always:

Accepted Answer

π (pi)

Answer

1

Answer

2

Answer

3.14

Question 51

Which shape encloses the largest area if they all have the same perimeter?

Accepted Answer

Circle

Answer

Square

Answer

Rectangle

Answer

Triangle

Question 52

A circle has a radius of 7 cm. What is the length of its diameter?

Accepted Answer

14 cm

Answer

3.5 cm

Answer

21 cm

Answer

7 cm

Question 53

A circular pond has an area of 154 square meters. What is the radius of the pond?

Accepted Answer

7 meters

Answer

22 meters

Answer

3.5 meters

Answer

14 meters