I want to model the volume and the surface area of the object that can be seen in the images below.
I realize that the objects (Shampoo and body wash bottles) are irregular and that I don't know their cross-sections at regular intervals. I don't have any equations for them. So, I reckon that the simple methods of integration cannot be employed. I was wondering if it is possible to model these bottles, somehow? I have heard software like GeoGebra and Logger Pro make it possible such modeling and volumetric analysis of irregular shapes. I have tried searching on the web, but am thoroughly confused.
I am simply looking for suggestions that can guide me on how I should proceed with this problem, and I am not looking for exact solutions.
P.S - I am not very proficient in mathematics, and am pursuing this project as a self-challenge project at high-school level.
Any kind of help, feedback, or suggestions is welcome!
Spare me if I have overlooked something very obvious. Thanks in advance.
Edit 1: Can I just simply paste the picture in logger pro, plot points along the boundary of the object, and do a curve fit. After the curve fit is predicted, I can simply revolve it around an axis to get an approximation.
Edit 2: The drawback of this method is that the approximation would be far from accurate as the shampoo bottles are far from being perfectly circular objects and so integrating solids of revolution method is not a good option. Any thoughts on the same?