How to prove formula for volume of cone ?

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As seen in the below image, the cone is divided into 2 triangles which can be proved similar by AA test.

l is the slant height of the cone, r is the radius

y is the radius of the disc on the smaller triangle with x as height

Using similarity

r            h                          rx

__ =  ______  =>        y =  ________

y           x                            h

By integration its easy to see that volume of cone is summation of smaller discs with area

integrated over the interval 0 to h

Volume of cone =

=>

=>

=>

=>

=>

Hence proved, volume of cone is =

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