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# Area of the shaded portion in given figure isA) $7.5 \pi$ square unitsB) $6.5 \pi$ square unitsC) $5.5 \pi$ square unitsD) $4.5 \pi$ square units

Last updated date: 20th Jun 2024
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Hint:
We can observe two semicircles with the same center but different radii. We have to find the area of the shaded portion. For that we have to remove the area of the inner semi circle from the area of outer semicircle.
Area of semicircle = $\dfrac{{\pi {r^2}}}{2}$

Complete step by step solution:
Let the radius of inner semicircle be $r = 5-1=4$ units

Radius of outer circle be R = 5 units
$\Rightarrow A\left( {outer{\text{ }}semicircle} \right) - A\left( {inner{\text{ }}semicircle} \right)$
$\Rightarrow \dfrac{{\pi {R^2}}}{2} - \dfrac{{\pi {r^2}}}{2}$
Taking $\dfrac{\pi }{2}$ common
$\Rightarrow \dfrac{\pi }{2}\left( {{R^2} - {r^2}} \right)$
$\Rightarrow \dfrac{\pi }{2}\left( {{5^2} - {4^2}} \right) \\ \Rightarrow \dfrac{\pi }{2}\left( {25 - 16} \right) \\ \Rightarrow \dfrac{{9\pi }}{2} \\ \Rightarrow 4.5\pi sq.units \\$
Hence the area of the shaded portion is $\Rightarrow 4.5 \pi sq.units$.