Question

(PLSSS HELP!!) Explain how the formula for the area of a square is related to the formula for the volume of a cube.

Answer 1

x = side length

Area of a square = x^2

Area of a cube = x^3

The squaring operation is directly tied to the geometric shape of a square. The naming is not a coincidence. The same can be said about the cubing exponent being connected to a 3D cube in geometry.

Notice how x^3 can be written as x^2*x. Buried inside the volume of a cube formula is the area of a square. We can effectively rewrite that second equation as

volume of a cube = (area of a square)*x

where x is the side length of the cube and square

This idea of tying together the volume and area like this will be helpful when setting up other volume formulas (eg: volume of a prism).