In the figure, the area of the shaded segment is
-
A.
3(pi) -
B.
9(frac{sqrt{3}}{4}) -
C.
3 (pi – 3 frac{sqrt{3}}{4}) -
D.
(frac{(sqrt{3 – pi)}}{4}) -
E.
(pi + frac{9 sqrt{3}}{4})
Correct Answer: Option C
Explanation
Area of sector = (frac{120}{360} times pi times (3)^2 = 3 pi)
Area of triangle = (frac{1}{2} times 3 times 3 times sin 120^o)
= (frac{9}{2} times frac{sqrt{3}}{2} = frac{9sqrt {3}}{4})
Area of shaded portion = 3(pi – frac{9sqrt {3}}{4})
= 3 (pi – 3 frac{sqrt{3}}{4})