Results 1 to 3 of 3

Math Help - double a cubes volume

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    9

    double a cubes volume

    I know that to double the volume of a cube multiply each dimension by the cubic root of 2 (about 1.26). I worked it out myself but cannot explain it to my fellow student teachers why it is. Any help appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Like a stone-audioslave ADARSH's Avatar
    Joined
    Aug 2008
    From
    India
    Posts
    726
    Thanks
    2
    Let the side of the cube be a,
    Now If you double volume but keep it as a cube (with the new side length as b)
    then
    b^3 = 2a^3
    Hence
    b= 2^\frac{1}{3} a
    And so is your answer
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Area and volume

    Hello rick_rine
    Quote Originally Posted by rick_rine@yahoo.com View Post
    I know that to double the volume of a cube multiply each dimension by the cubic root of 2 (about 1.26). I worked it out myself but cannot explain it to my fellow student teachers why it is. Any help appreciated.
    If you'd like a way of looking at situations like this that doesn't involve algebra, and is perhaps a little more intuitive, then look at it like this.

    A volume always involves (length) x (length) x (length), whether it's the volume of a cube, a cone, a sphere, or whatever. So similar solids (i.e. solids with the same proportions, but different measurements) will have volumes that vary according to the cube of their lengths.

    For example, if we make a model that is one-sixth the size of the original, then the original's volume is 6 x 6 x 6 = 216 times as great as the model's.

    In a similar way, the area of two similar shapes varies as the square of their lengths. So in the case of our model, the original's surface area will be 6 x 6 = 36 times that of the model.

    When we work back from volume to length we must remember to use the inverse or 'opposite' operation to cubing: that is, finding the cube root. So, if we halve the volume - in other words we divide it by 2 - we will need to divide the lengths by the cube root of 2.

    Similarly, working back from area to length will involve a square root. So, if an area is halved, then lengths will be divided by the square root of 2.

    I hope that this explanation may supplement ADARSH's reply and provide a 'feel' for what is happening here.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding volume using a double integral?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 8th 2009, 06:11 PM
  2. Volume of Solid and Double Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 6th 2009, 12:36 PM
  3. volume of solid using double integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 19th 2009, 05:00 PM
  4. Volume by double integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 26th 2009, 01:05 AM
  5. Double integral:volume
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2008, 04:23 PM

Search Tags


/mathhelpforum @mathhelpforum