I need to find the volume of a solid of revolution. For the cross section, I don't have the formula (for example, y = Ax), I just have some points (for example, 2 vectors with the same size). Based on what I have, I can create a a graph in 2D. After that I should "rotate" this figure and get a solid of revolution, which I need to get its volume.
a = [1 2 3 4 5 6 7 8 9 10]
b = [1 1,5 2 2,5 3 3,5 4 4,5 5]
After getting these 9 points, I can create this graph:
After creating the graph, I can rotate it like the image below (in blue, the line obtained by the graph; in red, the axes; in black, the rotation circle)
So, I get an 3D form and want to get its volume. How can I do it? Is there an precise way for it?
OBS: I thought about splitting it in multiple cilinders, but then it is not that precise when I have just a few points and gets way harder when the image is more complicated as the image below (because then I need to calculate some volumes to remove from a larger volume):
Since now, thanks for your time.