In the figure,AB and CD are two diameters of | vedclass

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(B) Radius $(r_1)$ of the larger circle $= 7 \, cm$.Radius $(r_2)$ of the smaller circle $= \frac{7}{2} \, cm = 3.5 \, cm$.Area of the smaller circle

Vedclass · Accepted Answer

$66.5$

Vedclass · Answer

(B) Radius $(r_1)$ of the larger circle $= 7 \, cm$.Radius $(r_2)$ of the smaller circle $= \frac{7}{2} \, cm = 3.5 \, cm$.Area of the smaller circle $= \pi r_2^2 = \frac{22}{7} 	imes 3.5 	imes 3.5 = 38.5 \, cm^2$.Area of the semi-circle $ACB$ of the larger circle $= \frac{1}{2} \pi r_1^2 = \frac{1}{2} 	imes \frac{22}{7} 	imes 7^2 = 77 \, cm^2$.Area of $	riangle ABC = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes AB 	imes OC = \frac{1}{2} 	imes 14 	imes 7 = 49 \, cm^2$.Area of the shaded region $=$ Area of the smaller circle $+$ (Area of semi-circle $ACB - 	ext{Area of } 	riangle ABC$).Area of the shaded region $= 38.5 + (77 - 49) = 38.5 + 28 = 66.5 \, cm^2$.

In the figure,$AB$ and $CD$ are two diameters of a circle (with centre $O$) perpendicular to each other. $OD$ is the diameter of the smaller circle. If $OA = 7 \, cm$,find the area of the shaded region in $cm^2$. [Use $\pi = \frac{22}{7}$]

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