Geometry and TrigonometryMediumArea of a sector
Geometry and Trigonometry practice question
A circle has an area of 36π square inches. What is the area, in square inches, of a sector with a central angle of 30°? (Give your answer as a multiple of π, written without the π symbol.)
Answer: 3
30° is 1/12 of the full 360°, so the sector is 1/12 of the area: 36π/12 = 3π. The answer as a multiple of π is 3.
Common wrong answers
- If you answered 6
- 6 uses 1/6 of the circle (a 60° sector).
- If you answered 12
- 12 divides 360 by 30 — that's how many sectors fit, not the area of one.
- If you answered 1080
- 1080 multiplies 36 by 30 without dividing by 360.
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