Finding the volume of 3D objects using Riemann Sums
My class started this not too long ago and my teacher gave us this really weird equation to help find volume in irregular 3D objects, such as taking the Riemann sum of a circle protruded cylinder-wise with a sloping end face and a flat end face to find the volume. I took one look at it and figured, "Hey! Why not just take the integral of the slope and multiply it by the area of the flat polygon base? That way, it is height x width x depth." Now I know it won't work for every irregular object, like a circular hourglass object that changes to a square hourglass halfway through, but I would like to know if my idea at least works with the first shape, or if I am simply crazy and should stick with the textbook equation.
Thanks for reading and thank you even more if you reply. No hard feelings if you think I have lost my glass 4/3 pi r^3 's. (marbles)
My class started this not too long ago and my teacher gave us this really weird equation to help find volume in irregular 3D objects, such as taking the Riemann sum of a circle protruded cylinder-wise with a sloping end face and a flat end face to find the volume. I took one look at it and figured, "Hey! Why not just take the integral of the slope and multiply it by the area of the flat polygon base? That way, it is height x width x depth." Now I know it won't work for every irregular object, like a circular hourglass object that changes to a square hourglass halfway through, but I would like to know if my idea at least works with the first shape, or if I am simply crazy and should stick with the textbook equation.
Thanks for reading and thank you even more if you reply. No hard feelings if you think I have lost my glass 4/3 pi r^3 's. (marbles)
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