Urgent... Need volume of cylinder with varying diam. by f(x)

[kdt511]

I need to find the Sigma Max, which is equal to Force/Area.

It is a cylindrical cone with a height of 360ft.

The diameter varies by height with a height of 'x':

d=29.36-.352x+.00035x^2
The thickness of the wall is 1.5ft along the entire height.

The cylindrical tower is shaped liked this:
_
)_(


So, I need the equation for Sigma, which is Force/Area. The Force is equal to (150 times the equation for volume), as the Force is just the weight of the tower and 150 is the weight density. I'm not sure what the area would be.

Any help whatsoever would be GREATLY appreciated. Thanks

 

[Gene]

I think some clarification is required.
A cylinder is a space figure having two congruent circular bases that are parallel.
A cone is a space figure having a circular base and a single vertex.
I don't know what a cylindrical cone is but your sketch doesn't match either of these definitions. It looks as though you are trying for an hourglass shape but your equation d=29.36-.352x+.00035x^2 only works for a height from 0 to about 90 feet, not to 360 feet. Otherwise either the height or diameter is negative.
It isn't clear if the wall thickness is included in the volume at that weight density.
The hourglass shape would require rotating a hyperbola and would use a different volume formula than a cone or a cylinder.

Gene