Find the area of the shades segments in the figure
Attached Figure / Diagram
A
\(\sqrt{3}
B
4 \(\pi - \sqrt{3}\)
C
-\(\frac{2}{3} \pi\)
D
\(\frac{2\pi}{3}\) -3
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Area of section = \(\frac{60^o}{360^o}\) x 11r2
= \(\frac{60}{360} \times \pi \times 2^2\)
= \(\frac{1}{6}\) x 4
= \(\frac{4\pi}{6}\)
= \(\frac{2\pi}{3}\)
Area of triangle = \(\frac{1}{2x}\)
= 2 x 28.......60
Segment Area = Area of section - Area of triangle
= \(\frac{2\pi}{3}\) -3
Source: Myschool Past Questions Archive (Record #32752)