Circles

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Q1. If a circle has a radius of 3 cm, what is its circumference? (Use π = 3.14) (2023)

Solution:

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

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Q2. What is the radius of a circle if the circumference is 31.4 m? (2020)

Solution:

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

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Q3. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)

Solution:

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

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Q4. If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)

Solution:

Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².

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Q5. What is the angle subtended at the center of a circle by an arc of length 5 cm if the radius is 10 cm? (2022)

Solution:

Arc length = (θ/360) * 2πr; 5 = (θ/360) * 2π * 10; θ = (5 * 360) / (20π) = 30 degrees.

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Q6. What is the diameter of a circle with a radius of 9 cm? (2022)

Solution:

Diameter = 2 * radius = 2 * 9 cm = 18 cm.

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Q7. 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)

Solution:

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

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Q8. What is the area of a circle with a diameter of 16 cm? (2023) 2023

Solution:

Radius = diameter/2 = 16/2 = 8 cm. Area = πr² = π(8)² = 64π cm².

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Q9. What is the diameter of a circle with an area of 50π square units? (2017)

Solution:

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.

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Q10. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (Use π = 3.14) (2020)

Solution:

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