TheFixer

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8 years, 108 days

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These are replies submitted by TheFixer

Thanks to both of you for provoiding a different approach :)

@vv 

 

Thank you, i didnt think of that the cones hight was 1-y but ofcourse you are right, the total hight being 1 and the height of the cylinder being y

 

I got the same result as you did now applying lagrange multiplier as well.

@Kitonum 

 

Thanks!

The volume of the solid is represented by followin eq?

2*(1/3*Pi*r^2*h)+Pi*r^2*h

obtaining this formula  (5/3)*Pi*(x^2+y^2)*h

 

putting in your solution and the one i gave have very little impact on the solution.
 

maybe this formula is not right for the volume of the solid?

@vv 

Thanks allot for this solution.

I dont understand what all that syntax means, but when I enter the values into the formula for the volume of the solid i get the same as when i put x=y=(1/2)*sqrt(2)

If i approximate to 5 digits, if i approximate to 20 digits you solution will provoide 0,00000001xxxx bigger.

I guess that can be called insignificant and I can provoide a solution I understand. But the real solutin will be yours :)

 

The only thing left is to represent the solid with a graph

 

Applying lagrange multiplier I got that to maximize the volume y=+-(1/2)*sqrt(2)

Would make me happy if anyone can validate this solution.

Obtained eqyation to maximize this way:

r := sqrt(x^2+y^2);
Vcone := (1/3)*Pi*r^2*h;
Vcylinder := Pi*r^2*h;
Vtot := 2*Vcone+Vcylinder;

 

I managed to plot the hexagon, but i dont think it is a useful plot, at least i dont see how it helps me.

 

Edit, I have now plotted it againt the circle which makes the picture a bit more clear, but still i dont know how i can spin the heaxagon about the y-axis to make a solid, neither am I sure how to optimize its volume.

 

with(plots);
with(plottools);
X := .7; Y = .9;
p1 := plots[display](plottools[polygon]([[[-X, Y], [0, 1], [X, Y], [X, -Y], [0, -1], [-X, -Y], [-X, Y]]]), color = red, thickness = 2);
p2 := implicitplot(x^2+y^2 = 1, x = -1 .. 1, y = -1 .. 1);
display(p1, p2);

I fixed X and Y just to get a representation plot, is it possible to spin this plot around y-axis to make a solid?

 

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