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Topic: REALLY HARD CALCULUS MODELLING AND PROBLEM SOLVING QUESTION
Replies: 1   Last Post: Mar 7, 2013 6:46 AM

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Andreas Dieckmann

Posts: 93
Registered: 1/29/05
Re: REALLY HARD CALCULUS MODELLING AND PROBLEM SOLVING QUESTION
Posted: Mar 7, 2013 6:46 AM
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Hi, you build 1/6 of the volume by putting equilateral triangular bodies of side length a and thickness dh on top of each other such that the top corner and the two adjacent sides are aligned. The cross section of this arrangement will be semicircular if a=sqrt(r^2-h^2), where h is the height of the stack and r is the side of the body at the bottom.
Then the volume as function of height h is V = 6 Integral_0^h ( sqrt(3) (r^2-h^2)/4 ) dh, which is a little smaller than the volume of the half sphere of radius r if h is set to r.

Greetings Andreas



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