Question

find the area of shaded region ,if radii of the two concentric circles with centre O are 7cm and 14cm respectively and angle AOC=40°

Answer 1

Area of shaded region=π theta/360°(R^2-r^2)
=22×40°/7×360°(14^2-7^2)
=22/7×9(196-49)
=22×147/7×9
=22×7/3
=154/3cm^2 answer.
hope this will help you.

Answer 2

Answer:

Area of the shaded region =

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

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,

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

Now ,

Area of the shades region

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

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

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

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

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

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

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

Therefore,

Area of the shaded region =

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

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