A tank has the shape of an inverted circular cone (point at the bottom) with height 8 feet and radius 4 feet. The tank is full of water. We pump out water (to a pipe at the top of the tank) until the water level is 4 feet from the bottom. What is the work required to do?
The first drop is pumped 0 ft.
The last drop is pumped 4 ft.
Okay, let's define 't' as the distance from the top of the tank. This gives us a nice vertical distance function, d(t) = t
The first drop has enough friends to cover
The last drop has enough friends to cover
No vertical relationships are allowed in this inverted cone!
We need a radius function, r(t), such that r(0) = 4 and r(4) = 2. It's linear, so we're done, r(t) = 4 - t/2
Thus,
You just have to think it through. It isn't magic.
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