Hi
I'm currently teaching how to calculate volumes of revolution using integration,
for e.g. suppose f(x)=x^2 is rotated 360 degrees about the x-axis from x = 2 to x=4, the volume generated would be given by
Integral[Pi(f(x))^2,2,4]
What I'm trying to do is plot the generated volume for explanation and demonstration purposes.
some of the more complicated examples are something like,
The region bounded by the curve y=9-x^2, x=2 and the x-axis is rotated 2Pi radians about the y-axis, calculate the volume of the solid generated.
I know how to calculate the actual volume, but is there any easy way of plotting the solid formed in mathematica.
