Calculating sum of volume using r, theta, and z

I'm trying to calculate the volume of an irregular shape.
I am given numerous points with r, theta and z.
I need to create a command button to solve all the partial volume and add them up into a total volume.
I was thinking of using triple integral of r * dr * dtheta * dz but I'm not completely sure because that would simply become r^2 * theta * z and any points with zero would become zero.
Does anyone have a clue on how to solve these points and add them up into a total volume?
Any help would be appreciated!
File is attached.

This is an Excel Forum, not Math Forum, you have to explain the formulas you want apply

That's the thing. I was given no formula. My prof told me that there is no right or wrong answer? She told me this is what a company gives you to find the volume of a "laser scanned" object and I'm suppose to find a volume out of it. I'm not sure where to start..

certainly not from here, but the hope is the last to die

prefaces: I can't download your file, so I can't see what kind of data you have or how it is laid out. It has been a long time since I've this sort of thing in 3 dimensions, so my math is rusty. Even if I could easily see the solution to this homework problem, I wouldn't give it to you, because that would short circuit your learning process. I will try to make some observations and suggestions that will help point you in the right direction.

It would appear you are given a table of coordinates, which represents some function. Your task is to compute the volume of this function. It would appear that you want to use Riemann sums to do this, and you want to use cylindrical coordinates to do this.

That's the thing. I was given no formula.

But, you were given a table that represents that "formula"/function. One thing I see when students have trouble with this kind of problem is that they seem to get stuck thinking that a function has to be represented as an equation (eg f(x)=ax+b), so they don't know what to do when they aren't given an equation. Perhaps the "leap" you need to make is how to use a table as your representation of the function rather than an equation.