1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Surface areas

  1. Jan 22, 2004 #1
    I know that the equation for the surface area of any solid of revolution around, say, the x-axis is
    [tex] SA = 2\pi\int_{a}^{b} y\sqrt{1 + (\frac{\,dy}{\,dx})^2} \,dx [/tex]

    What I need is the same formula except in parametric terms, like if the problem was given in terms of x(t) and y(t). Any takers?
  2. jcsd
  3. Jan 22, 2004 #2
    If it revolves about the x-axis on the closed interval [a,b], then
    [tex]SA = 2\pi\int_{a}^{b} y(t)\sqrt{[x'(t)]^2 + [y'(t)]^2} \,dt [/tex]

    For example. if the surface are of the solid generated by revolving the region enclosed by the curve with parametric equations x(t), y(t) from t = 0 to t = pi/2, then the upper limit, b = pi/2, lower limit a = 0.

    If it revolves about the y-axis on the closed interval [a,b], then
    [tex]SA = 2\pi\int_{a}^{b} x(t)\sqrt{[x'(t)]^2 + [y'(t)]^2} \,dt [/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook