1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook