Determining the Surface Area of a Solid of Revolution

Key Questions

• How do I find the surface area of a solid of revolution using parametric equations?

  If a surface is obtained by rotating about the x-axis from `t=a` to `b` the curve of the parametric equation

  `{(x=x(t)),(y=y(t)):}`,

  then its surface area A can be found by

  `A=2pi int_a^by(t)sqrt{x'(t)+y'(t)}dt`

  If the same curve is rotated about the y-axis, then

  `A=2pi int_a^b x(t)sqrt{x'(t)+y'(t)}dt`

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  I hope that this was helpful.

  Wataru · · Oct 18 2014

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• Question #99004
• How do you find the surface area generated when the curve `y=sqrt(r^2-x^2), 0<=x<=a` is rotated about the x axis?