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Home » AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.
Areas Related To Circles | CBSE | Class 10 | Maths | NCERT
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.

Solution:

21 cm = Radius (R) of the larger circle,

 7 cm = Radius (r) of the smaller circle,

30°= Both concentric circles’ sectors form an angle.

Formula of sector = \frac{\theta }{{{360}^{\circ }}}\times \pi {{r}^{2}}

The area of the larger sector = (30°/360°)×πR2 cm2

= (1/12)×(22/7)×212 cm2

= 231/2cm2

The area of the smaller sector = (30°/360°)×πr2 cm2

= 1/12×22/7×72 cm2

=77/6 cm2

The area of shaded region = Area of the larger sector – Area of the smaller sector

The area of the shaded region = (231/2) – (77/6) cm2

= 616/6 cm2 = 308/3cm2

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