What is the volume of a cube with side measuring 9 m?

Answer 1

In Geometry we understand that the cubes 2D sister is called a Square. In order for a square to be defined as such it MUST contain 4 congruent line segments and create 4 congruent angles.

Now in 3D, all we've done to the square is added an additional plane of space. This additional plane of space allows for the 2D object to contain things such as fluids and solids.

It does not change the length of any objects. So when working with 2D objects we find area by multiplying length x width (or l x w). Which If we know one length of a square we understand that all line segments must be equal as well as angles.

However, in a 3D object, we've added an additional measurement called "Height". This again does not change the value of the measurement but instead gives the 2D object it's additional plane.

So In order for us to figure out the volume of a cube in which one side is 9m's long we need to write out a Postulate.

Volume of a Cube with one side being 9 meters

1) The definition of a cube is a 2 dimensional square with an additional plane of space

2) The additional plane of space does not change the measurement value

3) The additional plane of space presents a new value of called Height.

Now with this Postulate we can determine the value of any 3D cube with only one side.

So since a square's area can be determined by Length x Width and we know that a cubes area (or Volume as it's called with 3D objects) has to follow #3, in that it contains an additional value called Height.

Remember in a square (which a cube is made from) all lines and angels ARE CONGRUENT.

So Length (9m) x Width (9m) x Height (9m) = Area(Volume) of Cube at approximately 729m³