Results 1 to 2 of 2

Thread: open top cylinder

  1. #1
    Oct 2008

    open top cylinder

    A drum in the form of a circular cylinder and open at one of the circular ends, is to be made so as to contain one cubic yard. Find the dimensions of the drum (height h and base radius r) which minimizes the amount of material going into the drum. The surface area of the drum includes the area of the cylinder and the circles at the bottom.


    So far what I have tried to do is use the formulas for area of the circle and the cylinder and the put h in terms of r :

    1 cubic yard = pi*r^2 + 2*pi*r*h
    1 - pi*r^2 = 2*pi*r*h
    (1 - pi*r^2) / (2*pi*r) = h

    Then I put this back into the original formula:

    = pi*r^2 + 2*pi*r*(1 - pi*r^2) / (2*pi*r)

    In trying to differentiate I ended up with a very convoluted piece of paper that ended up with r = 9/pi and this is wrong.

    Can anyone tell me if the work I've posted so far is correct? It is possible that I just have a problem with the differentiation process, but also possible that I haven't set the problem up correctly.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas
    $\displaystyle \pi r^2h = 1$

    $\displaystyle h = \frac{1}{\pi r^2}$

    you want to minimize surface area ...

    $\displaystyle A = \pi r^2 + 2\pi r h$

    $\displaystyle A = \pi r^2 + 2\pi r \frac{1}{\pi r^2}$

    $\displaystyle A = \pi r^2 + \frac{2}{r}$

    now find $\displaystyle \frac{dA}{dr}$ and minimize the surface area
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Oct 30th 2010, 01:50 PM
  2. Replies: 2
    Last Post: Sep 26th 2010, 03:33 PM
  3. Replies: 1
    Last Post: Aug 10th 2010, 03:44 AM
  4. Optimization-Open Topped Cylinder
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Apr 13th 2010, 05:49 PM
  5. Inverse of an open set is open implies continuous
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Sep 14th 2009, 05:15 AM

Search Tags

/mathhelpforum @mathhelpforum