The question is as follows:
A swimming pool is being constructed so that it is the upper part of an inverted square‐based pyramid. Calculate H.
From this, I was wondering how I would calculate the original height of this pyramid, as though the pyramid hadn't been truncated?
Originally, I had come up with 1/3*64(3+x)= 1/3*64(3+x) – 1/3*16(3+x) using the volume formula of a pyramid, but this is definitely wrong and just typing it out I can see what I am trying to find it not clear (it was meant to be x, which is the 'added on' height to 3, which is what we already know).
As you can see I'm very confused.
So I'm just wondering how I would find H? This is a question for Year 10 students so I can't solve this question without a formula or method that is understandable for a student at that age and level.
Thanks in advance.
Best Answer
Hint: If you extend the sides to the point, each side now has two similar triangles, one that is all new and one that has the new part and the old part. The bases are in the ratio $4:8$, so the heights are in the ratio ???