I think that if you say "twice the size" of a 3D object, that SHOULD mean twice the volume. But many people say that meaning "twice the diameter" or "twice the length of a side".
If you want to be clear, you should use different words.
I read a book on statistics once that talked about misleading presentations of statistics. One example they gave was a graph that purported to show differences in income between various groups. The graph had a picture of a money bag for each group. And the HEIGHT of the money bag was proportional to the income of that group, e.g. if group X made twice as much money as group Y, then group X's bag was twice as tall. But, the writer pointed out, this gave a very misleading impression, because the bag in the picture was two dimensional, and so if X's bag was twice as tall, it would be 4 times the area. And the bags depicted 3-dimenstional objects, so X's bag would be 8 times the volume. It exaggerated the differences tremendously.