An architect designs a garden in a circular shape with centre E and radius 50 m. There is a flower bed ABCD of rectangular shape inside the garden as shown in the figure. Suppose length and width of the flower bed are 2x and 2y meters respectively.

Based on above information answer the following question:

If area of the flower bed is maximum, then area (in m²) of garden, which is outside the flower bed is:

2500 (π - 2) m²

The correct answer is Option 3: 2500 (π - 2) m²

Radius (r)=50

Area of circle (Garden) = $= πr^2$ = 50x50xπ =2500π

Maximum Flower Bed: Occurs when the rectangle is a square.

Diagonal $=\text{diameter}=100\text{ m}$.

Side of square ($s$) = 100 / $\sqrt{2}$ = $50\sqrt{2}$

Area of square = $s^2$ = $50\sqrt{2}$ x $50\sqrt{2}$ =5,000

Outside Area: 2500π−5000 = 2500(π−2) m²