Your formula looks right to me, if your intent is basically to draw a disc perpendicular to the x-axis for each point on the curve and then add up the area of all those discs to get the volume. I’m not sure, though, why this would be useful - when would you have a 3D (non-planar) curve that you wanted to revolve?

Hi,

Simple question but I don’t seem to find a formula for confirmation.

Suppose we have a curve y = f(x). The volume of revolution of this curve along the x axis is V = PI * Integral (y*y)dx = PI * Integral (f(x)*f(x))dx

If we use parametric coordinates, x = f(t), y = g(t), we end up with

V = PI * Integral( g(t) * g(t) * f ‘ (t))dt

Ok, all fine so far.

What about for a curve defined x = f(t), y = g(t), z = h(t). What is the volume of revolution of this curve along the x axis ? I cannot seem to find a formula. My guess is

V = PI * Integral ((g(t)*g(t) + h(t)*h(t))* f ‘ (t) dt

but I need this confirmed (book, web pagem anything)

thanks

radu