My 'Archimedes Proof'

I attempted my own proof for Archimedes' Sphere and Cylinder. It shows how the volume of a sphere will have exactly 2/3 the volume of the smallest cylinder it can fit inside. My proof worked and I was really proud of myself (hahaha) and here it is.

The volume of a sphere=4/3 πr^3

The volume of a cylinder=πr^2 h

Cylinder r= Sphere r 2r=d (diameter)

From the diagram you can see that the diameter of the sphere will be equal to the h

eight of the cylinder (h=d), and as d=2r, by the transitive property, h=2r.

If we substitute 2r for h in the cylinder formula, we get:

Vc=πr^2 2r

To make it clearer, let's break it

 up:

Vc=π x r x r x 2 x r

If we rearrange it we get:

Vc=2πr^3 

To finish our proof let's add in the sphere formula:

4/3 πr^3/2πr^3 

We cancel out πr^3 from top and bottom:

 

4/3/2

Multiply by 3/3:

4/6

Reduce:

4/6=2/3

  2/3

  

  Ta da!