question_answer

The maximum area of a rectangle that can be inscribed in a circle of radius 2 unit is (in square unit)

A)  \[4\]                                    

B)  \[8\pi \]

C)  \[8\]                                    

D)  \[5\]

Correct Answer: C

Solution :

The maximum area of a rectangle that inscribed in a circle is equal to the area of square whose diagonal length is 4 unit. Let the side of square be x unit. \[\therefore \]  \[{{(4)}^{2}}={{x}^{2}}+{{x}^{2}}\] \[\Rightarrow \]               \[2{{x}^{2}}=16\] \[\Rightarrow \]               \[{{x}^{2}}=8sq\,unit\]