Circles: Essential Concepts for Competitive Exam Success

Circles

Q. What is the distance between the center of a circle and a point on its circumference if the radius is 15 cm? (2014)

A. 15 cm
B. 30 cm
C. 10 cm
D. 5 cm

Solution

The distance from the center to any point on the circumference is always the radius, which is 15 cm.

Correct Answer: A — 15 cm

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Q. What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)

A. 8 cm
B. 12 cm
C. 10 cm
D. 6 cm

Solution

Using Pythagoras: (radius)² = (distance from center)² + (half chord)²; 10² = 6² + (half chord)²; half chord = 8 cm, so full chord = 16 cm.

Correct Answer: A — 8 cm

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Q. What is the length of a chord that is 6 cm from the center of a circle with a radius of 10 cm? (2019)

A. 8 cm
B. 12 cm
C. 10 cm
D. 6 cm

Solution

Using Pythagoras: chord length = 2√(r² - d²) = 2√(10² - 6²) = 2√(100 - 36) = 2√64 = 16 cm.

Correct Answer: A — 8 cm

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Q. What is the length of a diameter of a circle with a radius of 7 cm? (2022)

A. 14 cm
B. 21 cm
C. 7 cm
D. 28 cm

Solution

Diameter = 2 × radius; Diameter = 2 × 7 cm = 14 cm.

Correct Answer: A — 14 cm

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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021)

A. 10.47 cm
B. 12.57 cm
C. 15.71 cm
D. 20.94 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.

Correct Answer: B — 12.57 cm

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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021

A. 10.47 cm
B. 15.71 cm
C. 20.94 cm
D. 25.13 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.

Correct Answer: A — 10.47 cm

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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (Use π = 3.14) (2023)

A. 10.47 cm
B. 15.71 cm
C. 20.94 cm
D. 25.13 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.

Correct Answer: A — 10.47 cm

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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)

A. 2π cm
B. 4π cm
C. π cm
D. 8 cm

Solution

Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.

Correct Answer: A — 2π cm

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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)

A. 5.24 cm
B. 3.14 cm
C. 5.00 cm
D. 10.47 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. What is the length of an arc of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14) (2020)

A. 6.28 cm
B. 3.14 cm
C. 12.56 cm
D. 9.42 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 6 cm = 6.28 cm.

Correct Answer: A — 6.28 cm

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Q. What is the length of an arc of a circle with radius 5 cm and angle 60 degrees? (2020)

A. 5.24 cm
B. 3.14 cm
C. 5.00 cm
D. 6.00 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. What is the radius of a circle if its circumference is 62.8 cm? (2022)

A. 10 cm
B. 15 cm
C. 20 cm
D. 5 cm

Solution

Circumference = 2πr; 62.8 = 2πr; r = 10 cm.

Correct Answer: A — 10 cm

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Q. What is the radius of a circle if the area is 154 square units? (2023)

A. 7 units
B. 14 units
C. 11 units
D. 10 units

Solution

Area = πr²; 154 = 22/7 * r²; r² = 154 * 7/22 = 49; r = 7 units.

Correct Answer: A — 7 units

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Q. What is the radius of a circle if the circumference is 31.4 m? (2020)

A. 5 m
B. 10 m
C. 15 m
D. 20 m

Solution

Circumference = 2πr; 31.4 = 2πr; r = 31.4/(2π) ≈ 5 m.

Correct Answer: A — 5 m

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Q. What is the radius of a circle if the circumference is 62.8 cm? (2016)

A. 10 cm
B. 15 cm
C. 20 cm
D. 25 cm

Solution

Circumference = 2πr; 62.8 = 2πr; r = 62.8/(2π) ≈ 10 cm.

Correct Answer: A — 10 cm

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Q. What is the radius of a circle if the diameter is 14 cm? (2021)

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Solution

Radius is half of the diameter. Therefore, radius = 14 cm / 2 = 7 cm.

Correct Answer: A — 7 cm

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Circles

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