Oh yeah it's definitely a challenge. I had to do it for a project in 9th grade. It's my fault i picked it. I had to find the volume of "The Great Gherkin" in London.
Turns out, it required calculus. (solid of revolution is learned at calculus level) So i taught myself just that part of calculus to finish the project. Took me quite a while. (which is why it would make a great program)
Unfortunately, without using fluid displacement, it's impossible to get the exact size. (due to the disk method) However, you can get infinitely precise measurements but never exact.