# Math Help - double a cubes volume

1. ## 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.

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
$b= 2^\frac{1}{3} a$

3. ## Area and volume

Hello rick_rine
Originally Posted by rick_rine@yahoo.com
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.