Results 1 to 2 of 2

Math Help - applied max and min word problem

  1. #1
    Newbie beeliz's Avatar
    Joined
    Nov 2010
    From
    California
    Posts
    3

    applied max and min word problem

    I am not getting this type of problem.
    The question is: A soup can in the shape of a right circular cylinder of radius r and height h is to have a prescribed volume V. The top and bottom are cut from squares as shown in the figure (the figure is a circle inscribed in a square). If the shaded corners (the corners of the square outside of the circle) are wasted, but there is no other waste, find the ratio r/h for the can requiring the least material, including waste.

    In my book, it has steps for solving these problems. It says to draw a picture, then find a formula for the quantity to be maximized or minimized. Then using the conditions stated in the problem to eliminate variables, express the quantity as a function of one variable. Then find the interval of possible values from physical restrictions and solve.

    I know the formulas for volume and surface area of a cylinder: V= \pi r^2h and S=2 \pirh (that is the equation for surface area, right?). But I'm not sure exactly how to use them here.
    I know you need to get an equation with one variable in it, either r or h, and then take the derivative, but I don't know how r and h relate to each other in this problem.

    help please
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718
    Hi, and welcome to the forum.

    I don't know how r and h relate to each other in this problem.
    You are told that the can has to have a prescribed volume V. Using this fact, you can express, say, h as a function of an unknown r and a known constant V.

    After that, find the total area of metal that is needed to make a can of radius r and height h (note that the top and bottom are squares, not circles). Substitute h from the previous paragraph to get a function of r only. Using differentiation, find r in terms of V that gives the minimum of the function.

    Now you should have an equality on r and V. Substituting V=\pi r^2h, you get an equation on r and h, from where you can get the required ratio r/h.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] An Applied Trig/Max and Min Problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 10th 2012, 11:13 PM
  2. Applied max and min problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 9th 2009, 10:53 PM
  3. Help with a long applied DE problem.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 30th 2008, 12:29 PM
  4. Replies: 1
    Last Post: November 2nd 2008, 05:28 PM
  5. Applied problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 1st 2008, 05:44 PM

Search Tags


/mathhelpforum @mathhelpforum