Circles: Master Circumference, Area, and Arc Length

Question 1

Determine the length of the arc of a circle with a radius of 10 units and a central angle of 60 degrees. Express the answer in terms of π.

Accepted Answer

2π/3 units

Answer

π/3 units

Answer

π units

Answer

2π units

Question 2

A square is inscribed within a circle. If each side of the square measures 8 units, determine the radius of the circle.

Accepted Answer

4√2 units

Answer

8 units

Answer

16 units

Answer

32 units

Question 3

Calculate the area of a circle with a diameter of 12 cm.

Accepted Answer

144π cm²

Answer

12π cm²

Answer

72 cm²

Answer

144 cm²

Question 4

Given two circles with radii of 3 cm and 5 cm, respectively, find the ratio of their areas.

Accepted Answer

9:25

Answer

3:5

Answer

5:3

Answer

25:9

Question 5

A wheel with a radius of 14 cm makes 200 revolutions. What distance does the wheel travel?

Accepted Answer

56π cm

Answer

28π cm

Answer

5600 cm

Answer

2800 cm

Question 6

A square is circumscribed around a circle of radius 5 cm. Calculate the area of the square.

Accepted Answer

100 cm²

Answer

50 cm²

Answer

150 cm²

Answer

200 cm²

Question 7

The circumference of a circle is 10π cm. What is its area?

Accepted Answer

50π cm²

Answer

25π cm²

Answer

100π cm²

Answer

200π cm²

Question 8

An inscribed square has a side length of 4 cm. What is the area of the circle that circumscribes the square?

Accepted Answer

16π cm²

Answer

8π cm²

Answer

32π cm²

Answer

64π cm²

Question 9

Which of the following is a property of a circle?

Accepted Answer

All points on the circle are equidistant from the center.

Answer

The sum of the measures of the interior angles of a circle is 360°.

Answer

A circle can be inscribed in any triangle.

Answer

A circle has two axes of symmetry.

Question 10

A sector has an arc length of 10 cm and a central angle of 60°. What is the area of the sector?

Accepted Answer

5π/3 cm²

Answer

10π/3 cm²

Answer

15π/3 cm²

Answer

20π/3 cm²

Question 11

Calculate the circumference of a circle with radius r.

Accepted Answer

2πr

Answer

πr²

Answer

r/π

Answer

π/r

Question 12

What formula accurately calculates the circumference (C) of a circle, where r represents the radius?

Accepted Answer

C = 2πr

Answer

C = πr²

Answer

C = 4πr

Answer

C = πd

Question 13

Calculate the area (A) of a circle with a radius (r) of 5 centimeters.

Accepted Answer

A = 25π cm²

Answer

A = 50π cm²

Answer

A = 100π cm²

Answer

A = 25 cm²

Question 14

A circle is circumscribed around a square with sides measuring 8 centimeters. Calculate the circumference of the circle.

Accepted Answer

C = 32π cm

Answer

C = 16π cm

Answer

C = 64π cm

Answer

C = 128π cm

Question 15

Which formula calculates the area of a circle?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πd²

Answer

A = 4πr²

Question 16

Calculate the circumference of a circle with a radius of 10 inches.

Accepted Answer

20π inches

Answer

10π inches

Answer

50π inches

Answer

100π inches

Question 17

State the relationship between the radius and diameter of a circle:

Accepted Answer

Diameter = 2 * Radius

Answer

Diameter = Radius / 2

Answer

Radius = 2 * Diameter

Answer

Radius = Diameter / 2

Question 18

Define a tangent to a circle:

Accepted Answer

Touches the circle at one point

Answer

Intersects the circle at two points

Answer

Intersects the circle at one point

Answer

Parallel to the circle

Question 19

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

Accepted Answer

2πr

Answer

πr

Answer

πr²

Answer

2πr²

Question 20

If the radius of a circle is doubled, what happens to the area of that circle?

Accepted Answer

Quadruples

Answer

Doubles

Answer

Halves

Answer

Remains unchanged

Question 21

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

Accepted Answer

5 cm

Answer

2.5 cm

Answer

7.5 cm

Answer

10 cm

Question 22

A circle is circumscribed around a regular hexagon with side length 's'. What is the radius of the circle?

Accepted Answer

s√3/2

Answer

s

Answer

s/2

Answer

s√3

Question 23

What is the measure of an inscribed angle that intercepts an arc of 120°?

Accepted Answer

60°

Answer

30°

Answer

90°

Answer

120°

Question 24

An equilateral triangle is inscribed in a circle with radius 'r'. What is the length of each side of the triangle?

Accepted Answer

r√3

Answer

r

Answer

r√2

Answer

r√4

Question 25

A circle is circumscribed around a square with side length 's'. What is the area of the sector of the circle formed by the square?

Accepted Answer

s²π/4

Answer

s²/4

Answer

s²/2

Answer

s²π/2

Question 26

The area of a circle is given by the formula πr². What is the area of a circle with a radius of 10 cm?

Accepted Answer

100π cm²

Answer

10π cm²

Answer

20π cm²

Answer

200π cm²

Question 27

A sector of a circle has a central angle of 120° and a radius of 6 cm. What is the area of the sector?

Accepted Answer

18π cm²

Answer

12π cm²

Answer

24π cm²

Answer

36π cm²

Question 28

A circle has a diameter of 14 cm. What is the length of the radius?

Accepted Answer

7 cm

Answer

14 cm

Answer

28 cm

Answer

56 cm

Question 29

A semicircle has a diameter of 10 cm. What is the perimeter of the semicircle?

Accepted Answer

5π + 10 cm

Answer

10π + 5 cm

Answer

15π + 10 cm

Answer

20π + 5 cm

Question 30

Find the length of the arc intercepted by a central angle of 60 degrees in a circle with a radius of 5 centimeters.

Accepted Answer

2.5π cm

Answer

5π cm

Answer

10π cm

Answer

15π cm

Question 31

Which theorem states that a tangent line to a circle is always perpendicular to the radius drawn to the point of tangency?

Accepted Answer

Tangent Theorem

Answer

Pythagorean Theorem

Answer

Secant Theorem

Answer

Chord Theorem

Question 32

Which of the following equations represents the standard form of a circle with center (h, k) and radius r?

Accepted Answer

(x - h)² + (y - k)² = r²

Answer

(x + h)² + (y + k)² = r²

Answer

(x - h)² - (y - k)² = r²

Answer

(x + h)² - (y + k)² = r²

Question 33

Given two circles with radii r1 and r2, respectively, what is the condition for these circles to be congruent?

Accepted Answer

r1 = r2

Answer

r1 ≠ r2

Answer

r1 > r2

Answer

r1 < r2

Question 34

Which of the following statements describes a key property of all circles?

Accepted Answer

All points on a circle are the same distance from its center.

Answer

The diameter of a circle is twice its radius.

Answer

The area of a circle is calculated using the formula πr³.

Answer

A circle has exactly four points of tangency with any straight line.

Question 35

A circle has a radius of 5 cm. What is its circumference?

Accepted Answer

10π cm

Answer

25π cm

Answer

20π cm

Answer

5π cm

Question 36

An arc of a circle measures 120 degrees. If the radius of the circle is 6 cm, what is the length of the arc?

Accepted Answer

4π cm

Answer

6π cm

Answer

12π cm

Answer

3π cm

Question 37

A chord of a circle is 6 cm long, and the distance from the chord to the center of the circle is 4 cm. What is the radius of the circle?

Accepted Answer

5 cm

Answer

7 cm

Answer

3 cm

Answer

10 cm

Question 38

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

Accepted Answer

(50/3)π cm²

Answer

10π cm²

Answer

25π cm²

Answer

100π cm²

Question 39

A circle has a radius of 3 centimeters. What is its area?

Accepted Answer

9π cm²

Answer

27π cm²

Answer

81π cm²

Answer

3π cm²

Question 40

A square with a side length of 8 centimeters has a circle inscribed inside it. What is the area of the inscribed circle?

Accepted Answer

16π cm²

Answer

8π cm²

Answer

64π cm²

Answer

32π cm²

Question 41

What is the radius of the largest circle that can fit inside a square with a side length of 12 centimeters?

Accepted Answer

6 cm

Answer

12 cm

Answer

3 cm

Answer

9 cm

Question 42

A circle has a radius of 5 centimeters. What is its circumference? (Use π ≈ 3.14)

Accepted Answer

31.4 cm

Answer

15.7 cm

Answer

25 cm

Answer

78.5 cm

Question 43

A circle has a central angle of 60 degrees. What is the measure of the intercepted arc?

Accepted Answer

60 degrees

Answer

180 degrees

Answer

30 degrees

Answer

120 degrees

Question 44

A square is inscribed in a circle. The diameter of the circle is 12 cm. What is the side length of the square?

Accepted Answer

6√2 cm

Answer

6 cm

Answer

12 cm

Answer

8.49 cm

Question 45

A circle is circumscribed around a triangle. The radius of the circle is 10 cm. What is the length of the diameter of the circle?

Accepted Answer

20 cm

Answer

40 cm

Answer

5 cm

Answer

10 cm

Question 46

The circumference of a circle is 25π cm. What is its radius?

Accepted Answer

12.5 cm

Answer

25 cm

Answer

50 cm

Answer

6.25 cm

Question 47

An equilateral triangle is inscribed in a circle. The side length of the triangle is 6 cm. What is the radius of the circle?

Accepted Answer

2√3 cm

Answer

6 cm

Answer

4√3 cm

Answer

3 cm

Question 48

A circle has an area of 100π square meters. What is its diameter? (Use π ≈ 3.14)

Accepted Answer

20 meters

Answer

40 meters

Answer

5 meters

Answer

10 meters