Minimizing the Surface Area of a CanDate: 05/22/2000 at 03:42:43 From: Chris Donges Subject: Surface area What coke can dimensions would use the least amount of aluminum possible while still holding 375 ml? I'm not sure where to start - please help. Date: 05/22/2000 at 08:06:25 From: Doctor Jerry Subject: Re: Surface area Hi Chris, I'll have to make some assumptions. If the coke can can be thought of as a cylinder with two circular ends, then you can write two formulas: V = pi*r^2*h and S = 2*pi*r^2 + 2*pi*r*h. The second is the areas of the two ends plus the area of the cylinder. If r and h are in cm, you can convert 375 ml into cubic centimeters and then you'll have an equation like: 375*k = 2*pi*r^2 + 2*pi*r*h. You can solve this for h in terms of r. Substitute this into the formula V = pi*r^2*h, which now will be entirely in terms of r. Now, just maximize V. You can do this with calculus or graphing. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ |
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