Results 1 to 7 of 7

Math Help - World of Functions

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    World of Functions

    A open box with a square base is required to have a volume of 10 cubic feet.

    (a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.

    (b) How much material is required for a base 1 foot by 1 foot?
    Last edited by magentarita; July 20th 2008 at 09:47 AM. Reason: Changed Question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by magentarita View Post
    A open box with a square base is required to have a volume of 10 cubic feet.

    (a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.

    (b) How much material is required for a base 1 foot by 1 foot?
    Let h denote the height of the box. Then the volume of the box is:

    V = x^2 \cdot h = 10\ cft~\implies~ \boxed{h = \frac{10}{x^2}}

    The surface area of the box exists of 1 square and 4 congruent rectangles:

    A = x^2+4 \cdot h \cdot x Plug in the term for h from the first equation to eliminate h:

    A(x)=x^2+4 \cdot \frac{10}{x^2} \cdot x = x^2+\frac{40}x

    To calculate the extreme amount of material use the first derivation of A:

    A'(x) = 2x-\frac{40}{x^2} . Solve the equation A'(x) = 0 for x. For your confirmation only: x = \sqrt[3]{20} \approx 2.71\ ft
    Last edited by earboth; July 21st 2008 at 01:00 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Your x^2

    Where did x^2 come from?

    Also, isn't the volume of a box V = length times width times height?

    Where is this formula in your reply?

    Thanks,
    Rita
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by magentarita View Post
    Where did x^2 come from?

    Also, isn't the volume of a box V = length times width times height?

    Where is this formula in your reply?

    Thanks,
    Rita
    Your problem said: "A open box with a square base is ..."

    That means the length and the width are equal. Since one side of the square should have been labeled by x the area of the base is x^2 and the volume of the box is calculated by:

    volume = (base\ area) \cdot (height) or using one letter variable names:

    v = x^2 \cdot h
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Got It!

    I totally get it now.

    Good job! Thank you.

    This is a great site! I can meet great math teachers here and learn enough math to pass my course.

    Thank you very much.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    1

    Re: World of Functions

    so how do you express the ammount of material that is needed as a function of the length x. if u allready explained please elaborate
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: World of Functions

    We have:

    x^2h=V where V is a given constant. Hence:

    h=\frac{V}{x^2}

    The amount of material A is the area of the bottom and 4 sides:

    A=x^2+4xh and so:

    A(x)=x^2+4x\left(\frac{V}{x^2} \right)=x^2+\frac{4V}{x}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The World Population
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: July 14th 2009, 07:23 PM
  2. World of Functions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 6th 2009, 06:14 AM
  3. World Problems
    Posted in the Calculus Forum
    Replies: 14
    Last Post: December 7th 2007, 12:50 PM
  4. how in the world
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 19th 2007, 10:38 PM
  5. 2 more world problems (please help!!)
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 18th 2007, 07:53 PM

Search Tags


/mathhelpforum @mathhelpforum