Mathematical Formula For Volume

Length, Area, Volume - Do We Need Them?

An important tool one can use to understand different concepts is the question, "Do we need them?" Here, by "we", I mean all of humanity as a whole. That is, can you think of a scenario outside of the examination room where a person would feel the need to invent the concept in question? Of course, if a concept exists in the text books of today, the first person who invented it could not have possibly been motivated by doing good in an exam that tested that concept. It is often useful to imagine yourself in that person's shoes and think of the reason that led him to the discovery.

Let me demonstrate.

Volume. We all know that volume of a cuboid is length times breadth times height and volume of a sphere is four-thirds of pi times its radius cubed. But do we really need to define this quantity called volume? Do we really need all these formulas to compute it? Let's put ourselves in the shoes of a possible inventor of the concept.

Imagine you live in a world where no one knows how to compute the volume of different objects. The ruler of your kingdom is a man who takes interest in art and architecture. He visits his friend in Egypt and is fascinated by the pyramids. On his return, he summons you to the court and orders you to build an exact replica in your own kingdom. He also informs you that his good Egyptian friend has kindly agreed to supply you with one million bricks. Are one million bricks enough to build an exact replica?

It is clear that to answer such a question, you need to calculate the volume of the pyramid, the total volume of all the bricks combined and see which one is bigger. So, here we go. Here is one situation where you really need a formula for volume.