Results 1 to 4 of 4

Thread: Find volume of a cube as a function of diagonal length.

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    1

    Find volume of a cube as a function of diagonal length.

    Find the relationship describing the volume (V) of a cube as a function of the length of the diagonal going through the cube (d). and evaluate it for a diagonal length of d = 1.2.
    Last edited by mr fantastic; Sep 29th 2010 at 02:01 PM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    Quote Originally Posted by choy777 View Post
    Find the relationship describing the volume (V) of a cube as a function of the length of the diagonal going through the cube (d). and evaluate it for a diagonal length of d = 1.2.
    Pythagoras' theorem will give you this.

    If you have a regular cube of side length "x", the volume is $\displaystyle x^3$

    The diagonal across the base square has length $\displaystyle \sqrt{x^2+x^2}=\sqrt{2x^2}=\sqrt{2}x$

    The diagonal going through the cube has length $\displaystyle \sqrt{2x^2+x^2}=\sqrt{3x^2}=\sqrt{3}x$

    $\displaystyle \displaystyle\ V=x^3=\frac{\left(\sqrt{3}x\right)^3}{\left(\sqrt{ 3}\right)^3}$

    $\displaystyle =\displaystyle\frac{d^3}{\left(\sqrt{3}\right)^3}= \left(\frac{d}{\sqrt{3}}\right)^3$

    You can then perform your calculation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2010
    Posts
    1

    Lost

    I got lost how did it end up over root3 cubed
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    Quote Originally Posted by deadman View Post
    I got lost how did it end up over root3 cubed
    After applying Pythagoras' theorem twice, we get... "internal diagonal"= $\displaystyle x\sqrt{3}$

    where "x" is the length of a side of the cube.

    The volume of the cube is $\displaystyle x^3$

    Since $\displaystyle \displaystyle\frac{\sqrt{3}}{\sqrt{3}}=1$

    then $\displaystyle \displaystyle\frac{(x\sqrt{3})^3}{(\sqrt{3})^3}=x^ 3$

    which is the cube volume.
    This allows us to express the cube volume as a function of the internal diagonal length.
    The internal diagonal goes from the bottom right-corner of the base of the cube to the
    top-left corner of the facing side,
    or from the bottom left-corner to the facing side's top right-corner.

    I'll be the first to admit that my sketch is not drawn well!
    The sides should appear to be the same lengths.
    Attached Thumbnails Attached Thumbnails Find volume of a cube as a function of diagonal length.-cube.jpg  
    Last edited by Archie Meade; Sep 30th 2010 at 11:50 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: Jan 9th 2012, 01:45 AM
  2. find each side of a cube - volume.
    Posted in the Geometry Forum
    Replies: 38
    Last Post: Dec 15th 2010, 01:22 PM
  3. Replies: 0
    Last Post: Oct 15th 2008, 04:05 AM
  4. Replies: 12
    Last Post: Jul 9th 2008, 01:26 AM
  5. Replies: 2
    Last Post: Mar 30th 2008, 01:54 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum