In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10 cm, and O is the centre of bigger circle.

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Solution

$A C = 54 c m$
$B C = 10 c m$
$A B = A C - B C = 54 - 10 = 44 c m$
Area of colored region = Area of large circle - Area of small circle
= $π (R^{2} - r^{2}) = \frac{22}{7} ({(27)}^{2} - {(22)}^{2}) [\frac{A B}{2} = r]$
= $\frac{22}{7} (729 - 484) = \frac{22}{7} \times 245 = 770 {c m}^{2}$

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