Question

The maximum area of a rectangle that can be inscribed in a circle of radius $2$ units is :

• A. $8$ sq. units
• B. $4$ sq. units
• C. $8\pi$ sq. units
• D. $4\pi$ sq. units

Answer 1

The correct option is A $8$ sq. units

the rectangle having diagonal as the diameter of the circle.

if $a,b$ are sides of rectangle then,

$a^2+b^2=4^2=16$

$area\left(A\right)=ab=a\sqrt{16-a^2}$ sq. unit

for area to be maximum,

$\frac{dA}{da}=0$ $\to a=\sqrt{8}$

$\text{maximum area}\left(A\right)=\sqrt{8}\times \sqrt{8}=8$ sq. units