Volume of a Cube
First we have to understand what the cube really is. So cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube could also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of 3-sided trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). A cube is the three-dimensional case of the more general concept of a hypercube, which exists in any dimension.
How to find the volume of a cube?
Recall that a cube has all edges the same length (Cube bounded by six square faces). The volume of a cube is found by multiplying the length of any edge by itself two times. So if the length of an edge is 6, the volume is 6 x 6 x 6 = 216
Or as a formula: volume = s^3 where:
s is the length of any edge of the cube. Why any? Because all cube edges is equall.
When we write volume = s^3, strictly speaking this can be read as "s to the power 3", but because it is used to calculate the volume of cubes it's often spoken as "s cubed".
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 0 thickness. So strictly speaking, the cube has 0 volume. When we talk about the volume of a cube, we really are talking about how much liquid it could 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 0 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 tell "the volume of a cube" to mean the same thing. But this is not strictly correct in the mathematical sense. What they often mean when they tell 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.
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