Question

28. Find the area of the shaded region if radii of two concentric circles are 7 and 14 cm
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Answer 1

Answer:

100% correct answer

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Answer 2

Answer:

Answer :- Area of the shaded region =

\frac{154}{3}\: cm^{2} 3

154 cm 2

Step-by-step explanation:

Given O is a centre of a concentric circles.

Let r =OB = 7cm

R = OA = 14cm

<AOC = 40°

We know that,

\begin{gathered}\boxed { Area \: of \: a \: sector \: \\= \frac{x}{360}\times \pi \times (radius)^{2}}\end{gathered}

Now ,

Area of the shades region

= Area of the sector AOC - Area of the sector ABD

= \frac{x}{360}\times \pi \times R^{2}-\frac{x}{360}\times \pi \times r^{2}

360x×π×R 2

− 360x×π×r2

=\frac{x}{360}\times \pi \times (R^{2}-r^{2})

360x×π×(R2−r2)

=\frac{40}{360}\times \pi \times (14^{2}-7^{2})

36040×π×(142−72)

=\frac{1}{9}\times \frac{22}{7} \times (14+7)(14-7)

91×7

22×(14+7)(14−7)

=\frac{1}{9}\times \frac{22}{7} \times 21\times 7

91×7

22×21×7

= \frac{154}{3}\: cm^{2} 3

154 cm 2

Therefore,

Area of the shaded region =\frac{154}{3}\: cm^{2} 3

154 cm 2

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Step-by-step explanation:

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