Question: A bowl is made by rotating \(y=a x^{2}\) around the \(y\) -axis. ( \(a\) is a constant)

1. The bowl is filled with water to a depth \(\mathrm{h}\). What is the volume of water in the bowl? (Your answer will contain a and \(h\) )
2. What is the area of the surface of water if the bowl is filled to depth \(\mathrm{h}\) ? (Your answer will contain a and h)
3. Water is evaporating from the surface of the bowl at a rate proportional to the surface area, with proportionality constant \(k\). Find a differential equation satisfied by h as a function of time, \(t\). (That is, find an equation for \(d h / d t\) )
4. If the water starts at depth \(h_{0}\), find the time taken for all the water to disappear.

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