Question 32

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Jambmaths question: 

In the diagram above are two concentric circles of radii r and R respectively with centre O. If $r=\tfrac{2}{5}R$, express the area of the shaded portion in term of $\pi $and R

Option A: 

$\tfrac{21}{25}\pi {{R}^{2}}$

Option B: 

$\tfrac{9}{25}\pi {{R}^{2}}$

Option C: 

$\tfrac{21}{23}\pi {{R}^{2}}$

Option D: 

$\tfrac{5}{9}\pi {{R}^{2}}$

Jamb Maths Solution: 

$\begin{align}  & \text{Area of the circle with radius}r=\pi {{r}^{2}}=\pi {{\left( \tfrac{2}{5}R \right)}^{2}}=\tfrac{4}{25}\pi {{R}^{2}} \\ & \text{Area of the circle with radius}R=\pi {{R}^{2}} \\ & \text{Area of the shaded portion}=\pi {{R}^{2}}-\tfrac{4}{25}\pi {{R}^{2}} \\ & =\pi {{R}^{2}}\left[ 1-\tfrac{4}{25} \right] \\ & =\pi {{R}^{2}}(\tfrac{21}{25}) \\ & =\tfrac{21}{25}\pi {{R}^{2}} \end{align}$

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