Apparently, the volume of this cone is $\frac{1}{16}\pi r^2h$. My question is why this is the case, can someone please geometrically explain the reason behind the $\frac{1}{16}$ bit. Thanks.
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@PichiWuana im not sure if this is relevant to obtain the 1/16 part but the radius is supposed to be proportional to the square of its height. – Joe Mar 20 '16 at 15:51
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Given variation of radius is second degree.
$$ (z/h)^2 = (y/r) $$
$$ V = \pi \int_0^h y^2 dz $$
Evaluating it
$$ V = \frac{\pi r^2 h} {5} $$
The given degree of " cone" parabola is too low.
If it is given as
$$ (z/h)^{15/2} = (y/r) $$
only then given result is ok.
Narasimham
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