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Given a cylinder's radius and height, $a$ and $z$, and given that $z\ll a$, what is it's volume without using $\pi$?

I was thinking that I could integrate to get the cylinder's circumference, and then divide this by the diameter to get $\pi$, but I haven't tried it yet. Is this correct?

  • 4
    Just out of curiosity, why do you want to avoid $\pi$?2012-11-13
  • 0
    You need $\pi$ to get the cylinder's circumference.2012-11-13
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    It is simply a mind-bender, a challenging question designed to make me think. However, every solution I've tried so far has not worked.2012-11-13
  • 0
    If the area of the base is $A$, the volume is $zA$. Or if the circumference is $C$ the volume is $aCz/2$2012-11-13
  • 2
    You could always take the Archimedes route: place it in a bowl full of water (or a measuring jug) and measure the volume of liquid displaced.2012-11-13
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    Or you could weigh it. Then carve a little cube out of it and weigh that.2012-11-13

4 Answers 4