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Q Liquid is being poured into a parabolic bowl at a constant rate of . The volume of the bowl is given by , where the equation of the parabola is , where y is the height of liquid in the bowl. Find the rate of increase of the height of the liquid in the bowl when the height is 10 centimetres.

A We can write Volume

is .

So, when y=10, we can evaluate which is the rate of change, which evaluates to be 6cm/s.