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Math Help - Applying derivatives

  1. #1
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    Feb 2008
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    Applying derivatives

    A soft drink can in the shape of a right circular cylinder is to have a capacity of 250mm^3. If the diameter of the can must be no less than 4cm and no greater than 8cm. Find the dimensions of the can that will use the least amount of material (include top, bottom, and side). What is the ratio of height to diameter for this can?

    Can someone help me set up this question?

    V = pi(r^2)(height)=250, I guess for the volume
    Least amount of material, I guess would be the surface area of all sides,

    So SA = 2(pi(r^2)) + (2(pi)r)height

    Dunno....some assistance would be appreciated
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  2. #2
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    Aug 2007
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    Yeah looks like the right track to me. Substitute the first equation into the second to eliminate the height term. Then differentiate the resulting equation to get the rate of change of SA with respect to r. Then find the 0's and check to make sure it's a minimum. If that radius times 2 falls in the required range of diameters it's done.
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