Circles

Q. A circle has a circumference of 31.4 m. What is its radius? (Use π = 3.14)

Solution

Circumference = 2πr; 31.4 = 2 * 3.14 * r; r = 5 m.

Correct Answer: A — 5 m

Q. A circle has a diameter of 10 m. What is its area? (Use π = 3.14)

Solution

Area = πr² = 3.14 * (5)² = 3.14 * 25 = 78.5 m².

Correct Answer: A — 78.5 m²

Q. A circle has a radius of 3 cm. What is the length of a chord that is 2 cm away from the center?

Solution

Using Pythagoras: chord length = 2 * √(r² - d²) = 2 * √(3² - 2²) = 2 * √(9 - 4) = 2 * √5 ≈ 4.47 cm.

Correct Answer: A — 2.83 cm

Q. A circle is inscribed in a square of side 8 cm. What is the area of the circle? (Use π = 3.14)

Solution

Radius of the circle = 4 cm; Area = πr² = 3.14 * (4)² = 3.14 * 16 = 50.24 cm².

Correct Answer: B — 25.12 cm²

Q. If the area of a circle is 154 m², what is its radius? (Use π = 22/7)

Solution

Area = πr²; 154 = (22/7) * r²; r² = 154 * (7/22) = 49; r = 7 m.

Correct Answer: B — 14 m

Q. If the radius of a circle is doubled, by what factor does the area increase?

Solution

Area = πr²; if radius is doubled, new area = π(2r)² = 4πr², so area increases by a factor of 4.

Correct Answer: D — 4

Q. What is the circumference of a circle with a radius of 7 cm? (Use π = 22/7)

Solution

Circumference = 2πr = 2 * (22/7) * 7 = 44 cm.

Correct Answer: A — 44 cm

Q. What is the diameter of a circle whose area is 50.24 cm²? (Use π = 3.14)

Solution

Area = πr²; 50.24 = 3.14 * r²; r² = 50.24 / 3.14 = 16; r = 4 cm; Diameter = 8 cm.

Correct Answer: A — 8 cm

Q. What is the length of an arc of a circle with a radius of 10 cm that subtends an angle of 60 degrees at the center?

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * (22/7) * 10 = 10.47 cm.

Correct Answer: A — 10.47 cm

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