Related Rates Inverted Pyramid with Square Base

Water is being poured into an inverted cone. Use related rates to determine how fast the height is rising.

[jcgmaudlin]

I always search for this gentleman's explanations when I'm stuck on my homework

[vaughnviljoen]

I have a question. If you use trig or any other method and calculate the actual size of the base that the pyramid would have at the current level of 2 cm full and use that the answer when differentiating the answer comes out differently. But if you use the same formula you get the same volume at 2 cm high v =(1/3)(0.8^2)(2) and v = (4/75)(2^3) of 0.42667 cm3. Why do the answers differ if you use the exact base of the new pyramid. It seems like it should give the same answer if you use v = (1/3)(0.8^2)h which gives 40=(1/3)(0.8^2)(dh/dt), when differentiated but it doesn't. This question might be silly to some but I don't get it.

[sarahrobison]

quick question, how did h become cubed from being squared?