Volume enclosed by a cube
Definition:
The number of cubic units that will exactly fill a cube
Try this
Drag the orange dot to resize the cube. The volume is calculated as you drag.
How to find the volume of a cube
Recall that a cube has all edges the same length (See Cube definition).
The volume of a cube is found by multiplying the length of any edge by itself twice.
So if the length of an edge is 4, the volume is 4 x 4 x 4 = 64
Or as a formula:
volume = s^{3}

where:
s is the length of any edge of the cube.


In the figure above, drag the orange dot to resize the cube.
From the edge length shown, calculate the volume of the cube and verify that it agrees with the calculation in the figure.
When we write volume = s^{3}, strictly speaking this should be read as "s to the power 3",
but because it is used to calculate the volume of cubes it is usually spoken as "s cubed".
Calculator
Use the calculator on the right to calculate the properties of a cube.
Enter any one value and the others will be calculated. For example, enter the side length and the volume will be calculated.
Similarly, if you enter the surface area, the side length needed to get that area will be calculated.
Some notes on the volume of a cube
Recall that a cube is like an empty box. It has nothing inside, and the walls of the box have zero thickness.
So strictly speaking, the cube has zero volume.
When we talk about the volume of a cube, we really are talking about how much liquid it can hold, or
how many unit cubes would fit inside it.
Think of it this way: if you took a real, empty metal box and melted it down, you would end up with a small blob of metal.
If the box was made of metal with zero thickness, you would get no metal at all. That is what we mean when we say a cube has no volume.
The strictly correct way of saying it is "the volume enclosed by a cube"  the amount space there is inside it.
But many textbooks simply say "the volume of a cube" to mean the same thing.
However, this is not strictly correct in the mathematical sense.
What they usually mean when they say this is the volume enclosed by the cube.
Units
Remember that the length of an edge and the volume will be in similar units.
So if the edge length is in miles, then the volume will be in cubic miles, and so on.
Related topics
(C) 2009 Copyright Math Open Reference. All rights reserved
