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Surface area of solid of revolution

Discussion in 'Mathematics' started by fudgesweets, Feb 22, 2011.

  1. fudgesweets

    fudgesweets New commenter

    If a curve is rotated 2Pi about the x-axis, a solid is formed.

    The volume of revolution is Pi int y^2 dx
    The surface area of revolution is 2Pi int y ds.

    I understand the formulae, what I dont understand is why for the surface area it is 'ds' instead of dx. ...surely you are finding the circumference of lots of circles, adding them up along the x-axis? That is what happens with vol of revolution where you adding up the areas of lots of circles along the x-axis....so you sum along the axis and thus should be using dx?

    There is a flaw in my understanding...what is it?
     
  2. Piranha

    Piranha Lead commenter

    Bother, I thought I'd invented it.[​IMG]
    I recently taught M3 centres of mass for the first time, so I'm getting used to the idea of working out which integral to do.
     

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