At the centre of a city's municipal park there is a large circular pool. A fish is released in the water at the edge of the pool. The fish swims north for 300 feet before it hits the edge of the pool. It then turns east and swims for 400 feet before hitting the edge again. What is the area of the pool?

The fish travels North for 300 m and on hitting the edge, travels East for 400 m. The directions North and East are perpendicular to each other. On connecting the initial and final positions of the fish in the tank, we get a right-angled triangle. 
The line AC subtends an angle of 90 degree on the circumference. Therefore, AC must be the diameter of the pond. 
Applying Pythagoras theorem, we get, 
$$AB^2 + BC^2$$ = $$AC^2$$
$$AC^2 = 300^2 + 400^2$$
$$AC = 500$$ m.
=> Radius of the pond = $$250$$ m.
Area of the pond = $$\pi*r^2$$
=> Area = $$62500\pi m^2$$.
Therefore, option A is the right answer.