Circles

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Q1. 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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Q2. What is the diameter of a circle if its area is 50π square units? (2017)

Solution:

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

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Q3. 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.

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Q4. A circle has an area of 154 cm². What is the radius? (2019) 2019

Solution:

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

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Q5. If a circle's radius is tripled, how does its area change? (2023) 2023

Solution:

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

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Q6. What is the area of a circle with a radius of 3 m? (2020)

Solution:

Area = πr²; = π * 3² = 28.26 m².

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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? (2021)

Solution:

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

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Q8. If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)

Solution:

Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.

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Q9. What is the length of a chord that is 6 cm from the center of a circle with a radius of 10 cm? (2019)

Solution:

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

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Q10. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)

Solution:

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