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(B) Given: Radius of the large circle $R = 7\, cm$.Diameter of the small circle is $OD = R = 7\, cm$,so its radius $r = 3.5\, cm$.Area of the small sh

Vedclass · Accepted Answer

$66.5$

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(B) Given: Radius of the large circle $R = 7\, cm$.Diameter of the small circle is $OD = R = 7\, cm$,so its radius $r = 3.5\, cm$.Area of the small shaded circle = $\pi r^2 = \frac{22}{7} 	imes 3.5 	imes 3.5 = 38.5\, cm^2$.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 semi-circle $ACB$ = $\frac{1}{2} \pi R^2 = \frac{1}{2} 	imes \frac{22}{7} 	imes 7 	imes 7 = 77\, cm^2$.Area of the shaded segment (excluding the small circle) = Area of semi-circle $ACB$ - Area of $	riangle ABC = 77 - 49 = 28\, cm^2$.Total shaded area = Area of small circle + Area of shaded segment = $38.5 + 28 = 66.5\, cm^2$.

In the adjoining diagram, $\overline{ AB }$ and $\overline{ CD }$ are diameters of $\odot( O , 7\, cm )$ perpendicular to each other. $A$ circle is drawn with diameter $\overline{ OD }$. Find the area of the shaded region. (in $cm^2$)

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