question_answer

If the area of a circle inscribed in a square is  \[9\pi \,\,c{{m}^{2}}\]then the area of the square is

A)  \[24\,\,c{{m}^{2}}\]

B)                     \[30\,\,c{{m}^{2}}\] 

C)  \[36\,\,c{{m}^{2}}\]

D)  \[81\,\,c{{m}^{2}}\]

Correct Answer: C

Solution :

Area of the circle\[=\pi {{r}^{2}}=9\pi \] \[\Rightarrow \]   \[{{r}^{2}}=9\] \[\Rightarrow \]   \[r=\sqrt{9}=3\,\,\text{cm}\] \[\therefore \]Side of the square \[=2\,r=6\,\,\text{cm}\] \[\therefore \]Area of the square \[=\text{sid}{{\text{e}}^{\text{2}}}=6\times 6=36\,\,\text{c}{{\text{m}}^{2}}\]