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由Sesto编辑：
8/21/2013 4:01:15 PM
5
Derivative Applications (Related Rates)
There is an inverted square pyramid with a height of 10 m. The side of the square is 13 m.
Someone decides to fill the pyramid with water, and does so at a rate of 10 m3 per second. How quickly is the water level rising when it reaches the top?
I understand I need to find dh/dt, and that dV/dt = dV/dh x dh/dt with dV/dt being 10.
In order to find dV/dh I need to express the volume of the pyramid as a function of only h in order to find the derivative. So if the volume of the pyramid is V = (1/3)(b^2)h, how do I express b^2 in terms of h?
I realize this might be futile to post this here, but anyone know of a better website for help with math problems like this one?
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2 回复由JLx24编辑： 8/21/2013 5:22:05 PMokay, I have an idea that should work. Since the pyramid maintains the same relative proportions (since all of the pyramids being made by the continued flow of water are similar pyramids) when it comes to the dimensions of the height and base, you can set up a relation given the overall dimensions. So b = 13, h = 10 => b/h = 13/10 => b = 13/10 h You should be able to go from there. Geometric proportions are used quite often in calculus but many students miss them.
