Surface area formula proof - integrate circumference of volume of revolution

Homework Statement

I believe this is intended to be a proof of the formula πrl, surface area of a cone.

Homework Equations

A complete volume of revolution gives you a cone - the height h is the x value on a graph, the radius r is the y value. The y intercept is zero, therefore y=r/hx . All integration is with lim h→0

The Attempt at a Solution

When I tried this, I got:
∫2πydx
=2π∫r/hx dx
=2πr/h∫x dx
=2πr/h ∫x2/2
=πrh! So why has this not worked? I need this to give πrl!