Computing the Volume of a Paraboloid | MIT 18.01SC Single Variable Calculus, Fall 2010
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very interesting imo, thanks
therealjordiano 4 days ago
Isn't this just the shell method, in terms of y? So you could've just went right to the integral right? This is just the entire idea behind the cylindrical shell method right? Except that would have a 2pi, so maybe not.
BER2ERKER 5 days ago
@TheDaekle Well from the H we get a two dimensional area, correct, but we are not missing it. The third dimension comes the parabola itself. If we were doing this to a a cylinder, we would get the extra dimension from the height. In this parabola, the "base" (the extra dimension) is held fixed by the fact that we did not provide a variable to change it [the steepness or what I am calling the "base"]. What I am trying to say is that the extra dimension comes from the coefficient (the 1/2 part).
AnalyticalInsanity 2 weeks ago
I'm sorry, I may be confused but, If "H" is a length (lets say measured in metres for ease), then "H^2" is an area in metres squared, meaning the units of the final figure suggest we've calculated an area and not a volume. Have I misunderstood something? genuine question, not a criticism, I'm just curious how this works...
TheDaekle 1 month ago
thanks, and you're the best....
mbausmani 1 month ago
What is up with these comments?! Anyway, thank you for Computing the Volume of a paraboloid.
purecodan 1 month ago
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willamricard 1 month ago