Here's what I make of it.

- - -

The tank is conical, clearly 6 units high, and it looks like it's roughly 4 units in 'radius' at the top.

Call the radius at height y . If and it runs linearly (as you'd expect), then in general

.

Using conservation of energy, the amount of work done to fill the tank to a height (call it ) is equal to the totalgravitational potential energyof the water in the container.

The gravitational potential energy is found byintegrating(calculus) over circular "slices" of water, at height and with thickness . (Let me know if you don't get this part; it's explained better with a diagram.)

The slice will have a volume

.

Itsmasscomes just from multiplying by the density of water, :

.

Finally, the potential energy of the slice is

(where I have substituted for .)

Then just integrate with respect to .

.

The answer to part a) is .

The answer to part b) is (as the tank was already filled to 4 units.)