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Q: Function for volume calculation

Does anyone have an idea on how to calculate the volume restricted by a
surface (or already have build a function for it). 
What I am basically have is a two variables (r and z) in the form F(r, z)
= 0 where F is a polynomial of degree 32 for z and degree 16 for r. Z is
the Z-axis variable and r is the radius (x^2 + y^2) and this basically
will have a symmetrical form around the z-axis. In other words, the
polynomial will be a line in the z-r or z-x plane and then this connected
line will revolute around z (a complete circle), I need to calculate its
volume. This is in the purpose of calculating the workspace of a robot. 
Please need help and would appreciate your time.
Can you please send your suggestions by email.
Thank you.
Pierre Awaragi.

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