A-LevelMathematicsDifferential equationsMay/June 2020Paper 3 Q1012 Marks
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 = ⅓π(3rh² – h³).
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