Making them spherical gives them a predictable volume. Since they know the isotope used and its density, knowing the exact volume tells you the exact mass of the sphere.
But a cube would be even more exacting, since the volume of a cube is LxWxH, and since L, W, and H can be rational numbers, you can have a volume that's a rational number. However, when you're dealing with something that's got a circular component, now you're adding an irrational number (pi) into the computation, and while the volume is going to be a finite number, it will still be irrational, and therefore somewhat less exact (on an infinitesimal level).
Mark
Couldn’t a gadget be made to actually count individual atoms into a single mass? Then when it’s counted off a few quadrillion or so, we have something we can weigh.
Not quite. They're also ensuring that the mass of the sphere is exactly 1 kg.
As the article said, the idea is to be able to define the kilogram in terms of atoms. Since they know the volume and the mass, they would know the density. And because they're using a near-perfect crystal, they can translate the density to the number of atoms in the sphere.
At that point, the definition of "kilogram" becomes "the mass of N atoms of silicon-28."
Yes, but:
"...with imperfections of less than 35 millionths of a millimeter."...it is NOT perfect. Close to perfect, but not exactly.
(God must be getting a good chuckle out of this endeavor!)