Results 1 to 4 of 4

Math Help - Max volume of box

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    US
    Posts
    9

    Max volume of box

    What size (square) corners should be cut from a rectangular piece of cardboard 12 by 18 inches in order to maximize the volume of the resulting box when folded up?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Max volume of box

    Quote Originally Posted by Roleparadise View Post
    What size (square) corners should be cut from a rectangular piece of cardboard 12 by 18 inches in order to maximize the volume of the resulting box when folded up?
    Let side of square=x When folded up box will be of length 18-2x, width 12-2x and depth x So V =x(18-2x)(12-2x)
    Multiply out, differentiate and put dV/dx=0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    US
    Posts
    9

    Re: Max volume of box

    Please show me what to do next; I'm stuck.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Max volume of box

    Multiplying out V=x(216-24x-36x+4x^2) =216x-60x^2+4x^3
    dV/dx=216-120x+12x^2 For maximum solve this=0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 18th 2011, 02:08 PM
  2. volume flux, mass flux and volume flo
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: June 7th 2011, 07:30 PM
  3. Replies: 1
    Last Post: May 14th 2010, 05:08 PM
  4. divergence = flux / volume is independant of the limiting volume
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2010, 08:31 PM
  5. Volume
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 10th 2007, 07:47 AM

Search Tags


/mathhelpforum @mathhelpforum