Geometry and Trigonometry practice question

Answer: B. 2π

A 90° angle is 90/360 = 1/4 of the full circle. The circumference is 2π(4) = 8π, so the arc is (1/4)(8π) = 2π. Choice C (4π) is the area of the matching sector, not the arc length.

Why the other answers are wrong

A. π

You used πr = 4π as the circumference and took a quarter of it. The circumference is 2πr = 8π, so the arc is (1/4)(8π) = 2π.

C. 4π

4π is the area of that quarter-circle sector, (1/4)π(4²), not a length. Arc length is (1/4) of the circumference 8π = 2π.

D. 8π

8π is the entire circumference. The 90° angle covers only 90/360 = 1/4 of it, so the arc is 2π.

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