Thread: How to calculate volume of a 3d graph

Is this possible to do in excel? I have a 3d graph created using (x,y,z) values in the form of a table. Now I want an estimate of the volume of that graph, something similar to calculating the integral of a 3d graph (area below the graph).

Is this possible to do? I'm thinking maybe using trapezoid rule but in 3D...

Thanks

The quick and dirty way given the data you have would be to sum the area that defines the z coordinates. =SUM(B2:AX32)

However when you consider coordinate 0,2 where there is 0,2,-5 and 0,2,21.3 this method becomes much more approximate. The volume is only as accurate as your data.

I don't have access to 2007, so I can't read your file, so what I have to add is based on not seeing the actual data. I will also add that it has been a long time since I took multi-variable calculus, so I'm a little rusty.

I'm thinking maybe using trapezoid rule but in 3D...

The Riemann sum concept can be extended to multi-variable cases. Rather than starting with the trapezoid rule, I'd probably start with something based on boxes, just because I know the volume of a box readily (length*width*height). This is essentially equivalent to extending the left-hand and right-hand sums to the 2 variable case. If you feel like you can get a better estimate of the volume using some kind of average, then that might be a useful calculation to do.

An approach that doesn't usually get covered in single variable calculus (probably because Riemann sums are fairly easy to do in the one variable case) is called the Monte Carlo method. You might look into that and see if that approach can be applied to your data set.