I liked it, but there was an error of word choice, I think.
At least to my understanding, if I understand the concept properly. Which is always dodgy when it comes to these dimensional topics, as who really understands anything?
For example, consider a circle inscribed in a square, so that it touches the squares walls. It covers 79% of the square's surface. If we consider the case in 3 dimensions, a sphere only occupies 52% of the ¿area? inside of a cube.
I assume you already realised that you must mean volume
Anyhow, sorry for being a grammar nazi, but it sounds horrible to say the area of a cube