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Surface area formula proof - integrate circumference of volume of revolution

  • #1

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!
 

Answers and Replies

  • #2
No-one?
 

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