Question: A water tank has the shape shown above, obtained by revolving the curve \(y=\frac{25}{4096} x^{4}\) from \(x=0\) to \(x=8\) about the \(y\) -axis, where \(x\) and \(y\) are measured in feet. Water flows into the tank at a constant rate of 250 cubic feet per minute.

1. Find the total volume of the tank. Indicate units of measure.
2. To the nearest minute, how long would it take to fill the tank if the tank was initially empty?
3. Let \(h\) be the depth, in feet, of water in the tank at any time \(t\). How fast is the depth of the water in the tank increasing when \(h=4\) feet? Indicate units of measure.
4. Suppose that while the tank is filling, it springs a leak at \(h=6\) feet, so that when the depth of the water reaches that level, water starts to trickle out of the tank at a rate of 15 cubic feet per minute. How fast is the depth of the water changing when \(h=16\) feet?

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