question_answer

In the adjoining figure PQRS is a rectangle \[8\,\,cm\times 6\,\,cm,\]inscribed in the circle. The area of the shaded portion will be.

A) \[48\,\,c{{m}^{2}}\]                        

B)  \[42.50\,\,c{{m}^{2}}\]

C) \[32.50\,\,c{{m}^{2}}\]                   

D)  \[30.5\,\,c{{m}^{2}}\]

Correct Answer: D

Solution :

\[PR=\sqrt{64+36}=\sqrt{100}=10\,\,cm\] Radius\[=\frac{10}{2}=5\,\,cm\] Now, Area \[=\pi {{r}^{2}}=\pi \times {{\left( 5 \right)}^{2}}=25\pi \] Area of shaded portion\[=\left( 25\pi -8\times 6 \right)\] \[=\left( 25\times \frac{22}{7}-48 \right)=\frac{550-336}{7}=\frac{214}{7}=30.5\,\,c{{m}^{2}}\]