Circles: Essential Concepts for Competitive Exam Success

Circles

Q. A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)

A. 8 cm
B. 10 cm
C. 12 cm
D. 14 cm

Solution

Using Pythagoras theorem: r² = (10/2)² + 6²; r² = 25 + 36 = 61; r = √61 ≈ 10 cm.

Correct Answer: B — 10 cm

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Q. A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)

A. 10 cm
B. 13 cm
C. 15 cm
D. 12 cm

Solution

Using Pythagoras theorem: r² = (5)² + (6)² = 25 + 36 = 61; r = √61 ≈ 7.81 cm.

Correct Answer: B — 13 cm

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Q. A circle has a diameter of 10 cm. What is its circumference? (2022)

A. 31.4 cm
B. 20 cm
C. 15.7 cm
D. 25 cm

Solution

Circumference = πd = π * 10 = 31.4 cm.

Correct Answer: A — 31.4 cm

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Q. A circle has a diameter of 20 cm. What is its circumference? (2022)

A. 62.8 cm
B. 40 cm
C. 31.4 cm
D. 20 cm

Solution

Circumference = πd = π * 20 = 62.8 cm.

Correct Answer: A — 62.8 cm

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Q. A circle has a radius of 10 cm. What is the diameter? (2020)

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

Solution

Diameter = 2 * radius = 2 * 10 cm = 20 cm.

Correct Answer: D — 20 cm

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Q. A circle has a radius of 12 cm. What is the diameter? (2020)

A. 6 cm
B. 12 cm
C. 24 cm
D. 18 cm

Solution

Diameter = 2 * radius = 2 * 12 = 24 cm.

Correct Answer: C — 24 cm

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Q. A circle has a radius of 3 cm. What is the diameter in millimeters? (2023)

A. 30 mm
B. 60 mm
C. 90 mm
D. 120 mm

Solution

Diameter = 2 * radius = 2 * 3 cm = 6 cm = 60 mm.

Correct Answer: A — 30 mm

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Q. A circle has a radius of 3 m. What is the diameter? (2022)

A. 3 m
B. 6 m
C. 9 m
D. 12 m

Solution

Diameter = 2 * radius = 2 * 3 m = 6 m.

Correct Answer: B — 6 m

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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)

A. 5.24 cm
B. 10.47 cm
C. 3.14 cm
D. 6.28 cm

Solution

Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.

Correct Answer: B — 10.47 cm

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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (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) * 2 * π * 5 = 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)

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 ≈ 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. A circle has an area of 154 cm². What is the radius? (2019)

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

Solution

Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.

Correct Answer: B — 14 cm

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Q. A circle has an area of 154 cm². What is the radius? (2019) 2019

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

Solution

Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.

Correct Answer: B — 14 cm

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Q. A circle has an area of 78.5 cm². What is its radius? (Use π = 3.14) (2019)

A. 5 cm
B. 7 cm
C. 10 cm
D. 12 cm

Solution

Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.

Correct Answer: B — 7 cm

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Q. A circle has an area of 78.5 cm². What is the radius? (Use π = 3.14) (2022)

A. 5 cm
B. 7 cm
C. 10 cm
D. 12 cm

Solution

Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.

Correct Answer: B — 7 cm

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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)

A. 78.5 cm²
B. 100 cm²
C. 50 cm²
D. 25 cm²

Solution

Radius = 10/2 = 5 cm; Area = πr² = π * 5² = 78.5 cm².

Correct Answer: A — 78.5 cm²

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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (Use π = 3.14) (2020)

A. 78.5 cm²
B. 50 cm²
C. 100 cm²
D. 25 cm²

Solution

Radius of the circle = side/2 = 10 cm / 2 = 5 cm. Area = πr² = 3.14 * 5² = 78.5 cm².

Correct Answer: A — 78.5 cm²

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Q. A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)

A. 50.24 cm²
B. 64 cm²
C. 25.12 cm²
D. 32 cm²

Solution

Radius = 8/2 = 4 cm; Area = πr² = π * 4² = 50.24 cm².

Correct Answer: A — 50.24 cm²

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Q. If a circle has a circumference of 31.4 cm, what is its radius? (2022)

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

Solution

Circumference = 2πr; 31.4 = 2 * π * r; r = 31.4 / (2 * π) = 5 cm.

Correct Answer: A — 5 cm

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Q. If a circle has a circumference of 62.8 cm, what is its radius? (2018)

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

Solution

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

Correct Answer: A — 10 cm

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Q. If a circle has a radius of 10 m, what is the diameter? (2021)

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

Solution

Diameter = 2 * radius = 2 * 10 m = 20 m.

Correct Answer: C — 20 m

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Q. If a circle has a radius of 3 cm, what is its circumference? (Use π = 3.14) (2023)

A. 6.28 cm
B. 9.42 cm
C. 12.56 cm
D. 15.70 cm

Solution

Circumference = 2πr = 2 * 3.14 * 3 = 18.84 cm.

Correct Answer: C — 12.56 cm

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Q. If a circle has a radius of 4 cm, what is its circumference? (Use π = 3.14) (2023)

A. 12.56 cm
B. 25.12 cm
C. 50.24 cm
D. 6.28 cm

Solution

Circumference = 2πr = 2 * 3.14 * 4 cm = 25.12 cm.

Correct Answer: A — 12.56 cm

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Q. If a circle has a radius of 4 cm, what is its diameter? (2022)

A. 4 cm
B. 8 cm
C. 12 cm
D. 16 cm

Solution

Diameter = 2 * radius = 2 * 4 cm = 8 cm.

Correct Answer: B — 8 cm

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Q. If a circle's radius is tripled, by what factor does the area increase? (2019)

A. 2
B. 3
C. 6
D. 9

Solution

Area = πr²; If r is tripled, new area = π(3r)² = 9πr²; Factor = 9.

Correct Answer: D — 9

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Q. If a circle's radius is tripled, how does its area change? (2021)

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
D. Remains the same

Solution

Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.

Correct Answer: C — Increases by 9 times

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Q. If a circle's radius is tripled, how does its area change? (2023) 2023

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
D. Remains the same

Solution

Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.

Correct Answer: C — Increases by 9 times

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Q. If the area of a circle is 78.5 cm², what is the radius? (2021)

A. 5 cm
B. 7 cm
C. 10 cm
D. 6 cm

Solution

Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.

Correct Answer: B — 7 cm

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Q. If the circumference of a circle is 31.4 cm, what is its radius? (2022)

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

Solution

Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.

Correct Answer: A — 5 cm

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Q. If the circumference of a circle is 31.4 cm, what is the radius? (2020) 2020

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

Solution

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

Correct Answer: A — 5 cm

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Showing 1 to 30 of 76 (3 Pages)

Circles

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