Question

In the given figure, one side of the ${30}^{\circ }$ inscribed angle is the diameter of a semicircle of radius 3 cm. What is the perimeter of the shaded region bounded by the inscribed angle and its intercepted arc?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

As arc(AC) makes ${120}^{\circ }$, therefore length of arc(AC) = $\left(\frac{1}{3}\right)\times \left(2\pi r\right)$
length of arc(BC) = semi-perimeter of the circle – length of arc(AC) =$\pi r-\left(\frac{2}{3}\right)\times \left(\pi r\right)=\frac{\pi r}{3}=\pi$ = 3.14cm
length of line segment(AC) = length of diameter(AB) $\times cos{30}^{\circ }$ $=6\times \left(\frac{\sqrt{3}}{2}\right)$= 5.2cm
perimeter of the shaded region = ( 3.14 + 5.2 + 6) cm = 14.34cm