Mensuration of 2D Shapes - Problems on Circles

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Q1. What is the circumference of a circle with a radius of 4 cm?

Solution:

Circumference = 2πr = 2π(4) = 8π ≈ 25.12 cm.

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Q2. What is the radius of a circle whose area is 113.04 cm²?

Solution:

Area = πr², so r = √(Area/π) = √(113.04/π) ≈ 6 cm.

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Q3. A circle is inscribed in a square with a side length of 6 cm. What is the area of the circle?

Solution:

Radius = side length / 2 = 6 / 2 = 3 cm. Area = πr² = π(3)² = 9π ≈ 28.26 cm².

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Q4. A circle has a diameter of 10 cm. What is its area?

Solution:

Radius = diameter / 2 = 10 / 2 = 5 cm. Area = πr² = π(5)² = 25π ≈ 78.5 cm².

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Q5. A circle has an area of 50.24 cm². What is its diameter?

Solution:

Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 4 cm. Diameter = 2r = 8 cm.

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Q6. If a circle has a radius of 3 cm, what is its diameter?

Solution:

Diameter = 2 × radius = 2 × 3 = 6 cm.

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Q7. A circle has a radius of 2.5 m. What is its circumference?

Solution:

Circumference = 2πr = 2π(2.5) = 5π ≈ 15.7 m.

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Q8. If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 60 degrees?

Solution:

Arc length = (θ/360) * 2πr = (60/360) * 2π(3) = (1/6) * 6π = π ≈ 3.14 cm.

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Q9. What is the radius of a circle if its area is 50.24 cm²?

Solution:

Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 5 cm.

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Q10. If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 90 degrees?

Solution:

Arc length = (θ/360) * 2πr = (90/360) * 2π(3) = (1/4) * 6π = 4.71 cm.