A curious proof of cone's volume

If you have seen lots of times the formula for the volume of a cone but weren't able to prove it, or you only demonstrate it years after you learned it; this is your video.

We'll introduce ourselves in a different proof, which you can do by yourself practically from scratch. Additionally, you will learn or refresh a few mathematical concepts and techniques which could be useful for you in the future.

PREREQUISITES AND BACKGROUND
A basic geometry intuition
Basic algebraic manipulation
Knowledge about common function plotting
The concept of limit (not epsilon-delta :))
How to formally write a generic polynomial
How to solve a linear system of equations

Note:
The expression for the Vn approximation and the polynomial form of the sum till n squared, should be proved by induction. You could try by yourself, and in case you have any doubt or want to share your results, contact the email below.

ERRORS
At 7:11 the 3rd coefficient in the 3rd row should be 3 instead of 2

00:00 Intro
00:30 Cylinders for the approximation and Thales's Theorem
02:08 Some approximations and 1st limit
04:29 How to find a function (for the sum in terms of n)
07:24 Final step of the proof

Email: [email protected]