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Homework Help: Differentials and area

  1. Jul 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is .04 cm thick.

    2. Relevant equations
    dz = (dz/dx) dx + (dz/dy) dy

    3. The attempt at a solution
    To find the area of the tin can we can see it as a rectangle. Since the diameter is given as 8cm, we can find the circumference 2(pi)r.
    Surface Area (SA)=height(h) x circumference(C)
    dSA=(dSA/dh) dh + (dSA/dC) dC
    dh = (.04)(2) = dC
    dSA=C(.08)+ h(.08)
    With this I can find the error in finding the surface area, but I don't know how to figure out what the total surface area is.
  2. jcsd
  3. Jul 8, 2008 #2
    Re: Differentials

    Oh actually if i use the equation V=(pi)r^2(h) I get the right answer...but am I just finding the max error in the calculated volume here? I understand that the derivative of volume=area, but in this equation doesn't dV=total differential=error? How could the value of the error also be the value of the area?
    Last edited: Jul 8, 2008
  4. Jul 8, 2008 #3
    Re: Differentials

    Try to layout the tin can as a map. That is, if you cut the edges and and layed everything flat. How would it look like?

    Or lookup the equation for the surface area of a cylinder.

    No, deriative of something is how much one thing changes in respect to another.
  5. Jul 8, 2008 #4
    Re: Differentials

    It's just gone midnight, so I maybe misreading your post, but why is calculus necessary? Surely, with the correct formulae for the area of a cylinder, then you're sorted.

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