Question related two different ways to do solution

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Homework Statement
An upside-down square pyramid with a height of 3 m and side lengths of 8m is filled to the brim with water. How much work is needed to lift all the water out of the container through the top. (ρ = 1000 kg/m3, g = 9.8 m/s2)
Relevant Equations
Work = Force * displacement
My work:
Screenshot 2025-04-12 203210.png


Answer Key (red font one) *may not be right.

My question is why is sidelength of cross section written as 8-8x/3, while my way of doing it doesn't involve that (involves suspicious similar triangle relationships)? Which answer (if any) is right here? 470 kj or 117 kj? Thank you!

Screenshot 2025-04-12 203210.png


Screenshot 2025-04-12 203309.png
 
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