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#1
04-08-2010, 01:33 PM
 SMS001 Junior Member Join Date: Apr 2010 Posts: 1 Rep Power: 0
Minimize the amount of steel used

I have a math problem that i need help on!! please!

There is a trough being made out of a sheet of steel. The trough will be a cylinder cut in half and have have a semicircular cross section. It is open along the rectangular face. The volume is 1000cm^3.

I need to find the radius and length of the trough which will minimize the amount of steel used.

#2
04-08-2010, 03:29 PM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 8,716 Rep Power: 17
Re: Minimize the amount of steel used

Quote:
 Originally Posted by SMS001 I have a math problem that i need help on!! please! There is a trough being made out of a sheet of steel. The trough will be a cylinder cut in half and have have a semicircular cross section. It is open along the rectangular face. The volume is 1000cm^3. I need to find the radius and length of the trough which will minimize the amount of steel used. I do not know where to start...please help!
*Write an expression for the volume of the half cylinder in terms of length and radius. Volume is fixed. Solve for either variable in terms of the other
*Write an expression for the surface area, of the cylinder, and eliminate one variable using the volume expression.
*You can plot this function and look for the minimum. If you have had calculus, Differentiate the expression (Minima and maximum occur at values where the derivative is zero), set equal to zero and solve. This will give you the value of one variable, for which the surface area of the trough is a minimum, but the volume constraint is met. Substitute in the volume equation to get the other variable.
#3
04-08-2010, 04:00 PM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,340 Rep Power: 12
Re: Minimize the amount of steel used

I love calculus.
#4
04-11-2010, 02:00 PM
 Mrs X can't count, can't spell! Join Date: Feb 2006 Location: New Zealand Posts: 2,296 Rep Power: 11
Re: Minimize the amount of steel used

Quote:
 Originally Posted by Robert Fogt I love calculus.
Stuff the calculus, i'm still struggling with the English!

and i wonder why you would try and minimise the steel used for a 1L "trough"?
#5
04-11-2010, 02:21 PM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 8,716 Rep Power: 17
Re: Minimize the amount of steel used

Quote:
 Originally Posted by Mrs X Stuff the calculus, i'm still struggling with the English! and i wonder why you would try and minimise the steel used for a 1L "trough"?
Probably calculus homework, although it is good manufacturing practice to use the minimum amount of material suitable for the job. IF that turns out to be a practical shape for the tray, it is the way to go, especially if you make a million of them.

"Homework" is so much more likely that I presented an outline to the solution rather than working the solution.

A better problem is to minimize the area of a rectangular sheet from which you can cut the rectangle and two half circles

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