Question

In Fig. 12.55 sectors of two concentric circles of radii 7 cm and 14 cm are given. Find the area of the shaded region if central angle is 60°. -7 cm 60° 14 cm DO -​

Answer 1

Answer:

Area of region OAB

$= \frac{60}{360} \times \pi \times {7}^{2} \\ \\ = \frac{1}{ { \cancel6} \: ^{3} } \times \frac{ \cancel{22} \: ^{11} }{ \cancel7} \times \cancel7 \times 7 \\ \\ = \frac{77}{3} {cm}^{2}$

Area of region OCD

$= \frac{60}{360} \times \pi \times 14 \times 14 \\ \ \\ \sf \: after \: simplifying \\ \\ = \frac{11 \times 2 \times 14}{3} \\ \\ = \frac{22 \times 14}{3} = \frac{308}{3}$

So area of shaded region =area of region OCD-area of OCD

$= \frac{308}{3} - \frac{77}{3} \\ \\ = \frac{1}{3} \times 23 = {77cm}^{2}$

Hope it helps you from my side

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