Question

ab and cd are respectively acrs of two concentric circle of radii 21 cm and 7 cm and centre o (see fig.12.32). if angle aob =30, find the area of the shaded region​

Answer 1

Answer:

102.667cm^2

Step-by-step explanation:

It is the 1/12 part of the circle as it is 30/360 part of the circle.

Hence area of shaded portion is

$(1/12)*\pi *(21^{2} -7^{2})\\ (1/12)*\pi *(441-49)\\(1/12)*\pi *392\\\\102.667cm^{2}$

Answer 2

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Radius of the larger circle, R = 21 cm

Radius of the smaller circle, r = 7 cm

Angle made by sectors of both concentric circles = 30°

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

= (1/12)×(22/7)×212 cm2

= 231/2cm2

Area of the smaller circle = (30°/360°)×πr2 cm2

= 1/12×22/7×72 cm2

=77/6 cm2

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

= 616/6 cm2 = 308/3cm2