UPSC CDS 1 2022 Math Paper

Given:
Three equal circles of radius 4cm touch each other
Formula Used:
Area of circle =πr2
Area of equilateral triangle =√3a2∕4
Where, r= radius of circle and
a= side of an equilateral triangle
Calculation:
According to the question
We can draw figure like this Now, From figure, we can say that
AB=BC=CA=8cm
So, △ABC is an equilateral triangle
And we know that angles of equilateral triangle is 60∘
Now, Area of shaded region= Area of △ABC - Area of sectors formed in three circles
⇒ Area of shaded region =‌

√3

4

(8)2−3×‌

60∘

360∘

π(4)2
⇒16√3−8π‌‌ square cm
∴ The area of shaded region is 16√3−8π squarecm.