UPSC 2013 CDS 2 Math Paper

ABCDEF is a regular hexagon.
∴∠AOB=

360°

6

=60°
Also, OA = OB = Radius of the circle.
⇒ ∠OBA = ∠OAB
So,∠OBA=∠OAB=∠AOB = 60°
(Using angle sum property of triangle)
∴ ΔOAB is an equilateral triangle.
x = Area of the circle – Area of regular hexagon
=

22

7

×52−6×

√3

4

×52
=78.57−64.95
=13.62cm2(approx)
So,13cm2<x<15cm2