using contour plot to solve the problem

Hi I want to use contour plot to find the minimum dimension of a can with the volume of 315, but I don't know how to do it. I'm sorry I'm pretty new to matlab

[darova]

Can you describe the form of a can? DO you have a picture?

[Dai Nguyen]

it has cylindrical shape with closed top

[Adam Danz]

What you mean by minimum dimension? A can has a height and a radius or diamter. How would color be used to find the minimum of those two dimensions?

[Dai Nguyen]

I want to reduce the cost for manufacturing the can by reducing the dimension of it, but still keeping the volume. I did the math with derivation and found that in order to minimize the cost the height has to be the same with the radius

[Dai Nguyen]

is there any way I can use contour plots to demonstrate it

[darova]

I think you need simple surf. Can you show your calculations?

[Adam Danz]

Yes, in the case of derivation, a smooth surface might be better than the 2D grid I suggested in my answer.

[Dai Nguyen]

Answer 1

[Adam Danz]

I assume you have an n-by-m matrix of costs for n heights and m radii.

I'd use heatmap or imagesc to create a gridded color display where x is can heights, y is radii (or the other way around) and the colorbar defines the cost.

[Dai Nguyen]

yes it will cost about a quarter to produce 1 meter, the dimension that I calculate to minimize the cost but still keeping the same volume is 4.645m for both height and radius