Volume of a Cube

Volume of a Cube

Using the definition of volume, we can calculate the sum of unit squares for any object with a closed space. In the case of a cube, a cube has a defined length, width and height.

In the simulation below, you can input an arbitrary length, width and height of your choice. To calculate the volume you can count each individual unit cubes to get the volume of a cube. Although we would get the correct answer, this is not practical as a cube with a large enough length, width, and height would take a long time to count up all the individual unit cubes each of length, width and height 1m by 1m by 1m.

Edge:

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An equation we can create therefore to calculate the volume of a cube is length width times height.

\[ V = l \times w \times h \]

Since we are dealing with a cube, this means that the length, width and height must all be equal in order to make it a cube. We can therefore simplify this equation by saying that the volume is the lengths, or sides of the cube cubed.

\[ V = s \cdot s \cdot s \]

or

\[ V = s^3 \]

Since a cube is an enclosed space in three dimensions, that would mean that the units would be meters cubed.

\[ m^3 \]

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