Answer:
9.78 u² . . . . . best matches selection B
Explanation:
The formula for the area of a segment is ...
A = (1/2)r²(θ-sin(θ)) . . . . . θ is the central angle in radians, r is the radius
Filling in the given values, we have ...
A = (1/2)·(6√3)²(π/3 -sin(π/3)) = 54(π/3 -√3/2) ≈ 9.7832960 u²
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Inappropriate rounding of intermediate computation values will give a different result. The value of π/3-sin(π/3) is the small difference of relatively larger numbers, so minor errors in the values of those numbers can have a great effect on the difference.