Geometry and Trigonometry practice question

Answer: B. 6π

A 60° angle is 60/360 = 1/6 of the circle. The full area is π(6²) = 36π, so the sector is (1/6)(36π) = 6π. Choice A (2π) is the arc length of that sector, not its area.

Why the other answers are wrong

A. 2π

2π is the arc length of the 60° sector, not its area. Take 1/6 of the full area 36π to get 6π.

C. 12π

12π is the full circumference of the circle (2π · 6), not a sector area. Use area: (1/6)(π · 6²) = 6π.

D. 36π

36π is the area of the entire circle. A 60° sector is only 60/360 = 1/6 of that, so the answer is 6π.

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