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Question: A tank for storing water is conical in shape, with maximum radius 20 m and maxi­mum depth 15 m. The large, circular end of the tank points vertically upwards and is open to the air. It is known that the volume of water in the tank will decrease at a rate proportional to the area of the water's surface, due to evaporation. Show that the water-level in the tank decreases at a constant rate. If the tank originally stores 1000 $\mathrm{m}^3$ of water and the water-level drops 1cm/day, how long will it be before the tank is empty? [Hint: A cone of base radius R and height h has a volume $\frac{1}{3}\pi R^2 h$].

My Problem: I have problem understanding what is meant by the area of the water's surface? is it the area of circle?

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Yes, that is what is meant. In context, that's made (fairly) clear because they're talking about evaporation, which happens (almost) entirely at the air-water boundary.

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