Book: RS Aggarwal - Mathematics
Chapter: 18. Area of Circle, Sector and Segment
Subject: Maths - Class 10th
Q. No. 30 of Exercise 18A
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30
In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.
Given:
Radius of inner circle = 3.5 cm
Radius of outer circle = 7 cm
∠POQ = 30°
Let the sector made by the arcs PQ and AB be S1 and S2 respectively.
Then, Area of shaded region = Area of S1 – Area of S2 ………….(i)
∵ Area of sector = 
× πr2
∴ Area of S1 = 
× 
× 7 × 7
= 
cm2
Similarly, Area of S2 = 
× 
× 3.5 × 3.5
= 
cm2
Thus, using (i), we have
Area of shaded region = 
- 
= 
= 
= 
cm2
Hence, the area of shaded region is 
cm2.
