Question

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

Answer 1

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.