What is the area of a circle sector with a 12 meter radius and a 42° central angle?
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Answer: C. 52.8 m2
Explanation
The area of a circle sector is found by multiplying the total circle area by the angle fraction. Dividing the forty two degree central angle by three hundred sixty degrees gives the proportional area factor. Multiplying this fraction by pi and the square of the twelve meter radius results in fifty two point eight square meters. A sector represents a pie shaped wedge of a circle enclosed by two radii and an arc. Central angles measure the proportional slice of a full three hundred sixty degree circular rotation. Circle area formulas require squaring the radius length before multiplying by the mathematical constant pi.
Option A underestimates the sector area by using an incorrect angular proportion multiplier. Option B represents a calculation error resulting from improper handling of the radius squaring step. Option D overestimates the area by applying a fraction larger than the actual central angle.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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