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Fish Swimming in Circular Pool

XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Geometry

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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?

  1. A.

    62500π62500\pi

  2. B.

    125000π125000\pi

  3. C.

    250000π250000\pi

  4. D.

    500000π500000\pi

  5. E.

    Cannot be answered from the given data.

Answer

A

Explanation

The North and East paths are perpendicular. The path forms a right-angled triangle inscribed in the circle, so the hypotenuse is the diameter of the circle. D2=3002+4002=250000  ⟹  D=500D^2 = 300^2 + 400^2 = 250000 \implies D = 500 feet. Radius R=250R = 250 feet. Area = πR2=π(250)2=62500π\pi R^2 = \pi (250)^2 = 62500\pi.

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