Circles

Q. A circle has a diameter of 10 m. What is its area?

Solution

Area = πr² = π(5)² = 25π m².

Correct Answer: B — 50π m²

Q. A circle has a radius of 3 cm. What is the diameter?

Solution

Diameter = 2r = 2(3) = 6 cm.

Correct Answer: B — 6 cm

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

Solution

Radius = 4 cm; Area = πr² = π(4)² = 16π cm².

Correct Answer: A — 16π cm²

Q. If a circle's radius is increased by 2 cm, what is the new area if the original radius was 4 cm?

Solution

New radius = 6 cm; New area = π(6)² = 36π cm².

Correct Answer: A — 36π cm²

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

Solution

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

Correct Answer: A — 5 cm

Q. If the radius of a circle is doubled, how does the area change?

Solution

Area = πr²; if r is doubled, area = π(2r)² = 4πr², which is quadrupled.

Correct Answer: D — It quadruples

Q. What is the area of a circle with a circumference of 31.4 cm?

Solution

Circumference = 2πr; r = 5 cm; Area = πr² = π(5)² = 25π cm².

Correct Answer: A — 25π cm²

Q. What is the length of an arc of a circle with a radius of 5 m and a central angle of 60 degrees?

Solution

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

Correct Answer: B — 5π/6 m

Q. What is the radius of a circle whose area is 36π cm²?

Solution

Area = πr²; 36π = πr²; r² = 36; r = 6 cm.

Correct Answer: A — 6 cm

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