I stumbled at that point too, but satisfied myself with a slightly more general argument than the first reply. Imagine the pyramid is made up of a bunch of sma

I stumbled at that point too, but satisfied myself with a slightly more general argument than the first reply. Imagine the pyramid is made up of a bunch of small but finite-size cubical blocks. Extending a block along any single axis doubles its volume. Extending all the blocks vertically at the same time doubles the height and volume of the pyramid, because the volume is just the sum of the volume of all the blocks. Mentally pass to the limit of small blocks, and you're there, or at least, I convinced myself I was there.