🚀 go-pugleaf

I believe i can answer your question, IF someone knows the answer to mine:

Take a cone, and cut it in two perpendicular to the base, with the cut not
passing though the point, now on the smaller piece will there be a curve or
straight line running from the point to the base, and if it is a curve what
is it's general equation, sqrt(x) or ln(x), or something else?

LMH

Gadget wrote in message
<909363956.9163.0.nnrp-02.c2de9192@news.demon.co.uk>...
>You have a Cylinder tank (L) in length, with two conical ends with their
>tips removed  lying horizontaly on a plinth. Liquid is poured into the
>cylinder from the filling point located on the top of the tank. based on
the
>height of the liquid in the tank I need a general formula with which to
>calculate the volume within the tank if I have the following information:-
>
>    1. The circumference of the tank (C)
>    2. Length of the cylinder section (L)
>    3. Height of the conical sections (H)
>    4. Diameter of the tank (D)
>    5. Diameter of the conical end which is removed (d)
>
>Any more questions please e-mail me at ghunter@blairgo.demon.co.uk
>
>

The equation of a cone (with longitudinal axis which
is the x-axis) is:

y^2 + z^2 = c^2 * x^2 where c is D/2H in this case.

So the equation for a slice through that (of constant
z value, say z=a) is:

y^2 = c^2 * x^2 - a^2

From that you should be able to get the area of the
top surface of a horizontal slice through the cone at
height a (from the axis of the cone) and then
integrate over the height parameter, a to get the
volume of the part in the cone end pieces.

I have more time tommorow. I'll have a crack at
actually turning the handle on the calculus

Ewen.



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