UPSC 2016 CDS I Math Paper

Let the radius of the bigger circle be r m.
∴πr2=707⇒r2=‌‌

707

π

m2
Diameter of the circle = AD = 2r m
AB = BC = CD (Given)
∴AB=

AD

3

=

2r

3

and AC=

2AD

3

=

4r

3

Area of the shaded region = 2(Area of semi-circle with AC as diameter – Area of semi-circle with AB as diameter)
=π(‌‌

4r2

9

−‌‌

r2

9

)
=π×‌‌

r2

3

=‌‌

707

3

m2
Therefore, cost of levelling the shaded region at the rate of ₹63/m2=

707

3

×63
=₹14,847