Mathematics (AS & A Level) · May / June 2020 · Paper 33 · Question 10

r A h A tank containing water is in the form of a hemisphere. The axis is vertical, the lowest point is A and the radius is r, as shown in the diagram. The depth of water at time t is h. At time t = 0 the tank is full and the depth of the water is r. At this instant a tap at A is opened and water begins to flow out at a rate proportional to h. The tank becomes empty at time t = 14. The volume of water in the tank is V when the depth is h. It is given that V = 1 3π3rh2 −h3 .

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