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(C) The shaded region is a sector of an annulus (a circular ring). The area of a sector of a circle with radius $r$ and central angle $	heta$ is give

Vedclass · Accepted Answer

$119.78$

Vedclass · Answer

(C) The shaded region is a sector of an annulus (a circular ring). The area of a sector of a circle with radius $r$ and central angle $	heta$ is given by $\frac{	heta}{360^\circ} 	imes \pi r^2$.Here,the shaded region is the difference between the area of the sector of the larger circle (radius $R = 28 \, cm$) and the area of the sector of the smaller circle (radius $r = 21 \, cm$),both with the same central angle $	heta = 40^\circ$.Area of shaded region = $\frac{	heta}{360^\circ} 	imes \pi R^2 - \frac{	heta}{360^\circ} 	imes \pi r^2$Area = $\frac{	heta}{360^\circ} 	imes \pi (R^2 - r^2)$Area = $\frac{40}{360} 	imes \frac{22}{7} 	imes (28^2 - 21^2)$Area = $\frac{1}{9} 	imes \frac{22}{7} 	imes (784 - 441)$Area = $\frac{1}{9} 	imes \frac{22}{7} 	imes 343$Area = $\frac{1}{9} 	imes 22 	imes 49$Area = $\frac{1078}{9} \approx 119.777... \, cm^2$Rounding to two decimal places,we get $119.78 \, cm^2$.

As shown in the diagram,the radii of two concentric circles are $21 \, cm$ and $28 \, cm$. If $m \angle AOB = 40^\circ$,find the area of the shaded region. (in $cm^2$)

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