Question: A bowl is made by rotating the curve y = ax2 around the y-axis (a is a constant).
(a) The bowl is filled with water to depth h. What is the volume of water in the bowl? (Your answer will contain a and h.)
(b) What is the area of the surface of the water if the bowl is filled to depth h? (Your answer will contain a and h.)
(c) 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 dh/dt.)
(d) If the water starts at depth h0, find the time taken for all the water to evaporate.