How do you compute the volume of a cat?
Dunking it in water doesn’t work– you only get the volume of the rat-like creature that lives inside the cat; much like the feeble alien within a Dalek. (And, if your answer had anything to do with contour integrals, get real.)
Here is a low-tech method that works: Using successive approximation, determine the smallest box that the cat will fully enclose itself in, and measure the size of that box. Cats tend to leave a few appendages hanging out of the corners– you may need to assist with folding the cat into the box for the final stages of approximation.
This cat is approximately 648 cubic inches in volume.