A vat (shown in attachment) contains water 2 m deep. Find work required to pump all water out of top of vat. (weight density of water = )

weight of water=

put my figure on the coordinate axis so I came up with general equation for the base, with respect to height (using a y=mx+b format):

but, I want to go down a positive depth, so I negated the equation:

---------------------------------(1)

As you can see, the above equation follows correctly, at a depth(h) of 0, we have a base of 2, at a depth(h) of 3 we have a base of 0, so the equation is valid, so far no mess-ups... I hope

Now, the general equation for a triangular volume is: Volume= (b=base, h=height, L=length)

But, because my equation for b is only taking one half of the triangle, I double it:

-------------------------------(2)

substituting (1) into (2) I get

L=6m so

therefore

W=130800

...which is exactly half of the answer, I just can't seem to find that missing 2 despite being so concise. I remembered to double the volume of my second figure to take into account the full triangle base. Please help me find this... it's so close