In the below figure, $ O A C B $ is a quadrant of a circle with centre $ O $ and radius $ 3.5 \mathrm{~cm} $. If $ O D=2 \mathrm{~cm} $, find the area of the shaded region.
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Given:

\( O A C B \) is a quadrant of a circle with centre \( O \) and radius \( 3.5 \mathrm{~cm} \).

\( O D=2 \mathrm{~cm} \).

To do: 

We have to find the area of the shaded region.

Solution:

Radius of the outer quadrant $R = 3.5\ cm$

Radius of the inner quadrant $r= 2\ cm$

This implies,

Area of the shaded portion $=$ Area of the outer quadrant $-$ Area of the inner quadrant

$=\frac{1}{4} \pi \mathrm{R}^{2}-\frac{1}{4} \pi r^{2}$

$=\frac{1}{4}(\mathrm{R}^{2}-r^{2})$

$=\frac{1}{4} \times \frac{22}{7}[(3.5)^{2}-(2)^{2}]$

$=\frac{11}{14}(3.5+2)(3.5-2)$

$=\frac{11}{14} \times 5.5 \times 1.5$

$=6.482 \mathrm{~cm}^{2}$

The area of the shaded region is $6.482\ cm^2$.

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Updated on: 10-Oct-2022

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