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
I was having the same thought - pi is irrational and goes on forever. Why not make the object a cube?
The answer may be the delicacy of the shape. They're looking for something that doesn't erode or deteriorate and that will maintain its mass to an exquisitly precise standard, so durability is a requirement, and the sphere is smooth and resistant to accidental damage. The cube or other block shape would have extremely sharp and delicate edges. I'm thinking of knocking the corner off a concrete block vs chipping a piece from a cannonball.
And the sphere is defined by ONE dimension.... radius.
Cubes are not optimal for this. First off, the edges of the cube would be ragged. You'd get great deal of uncertainty.
Second, physical, solid cubes are not really cubes -- they deform under stress. (I had a professor derive this mathematically back in college -- I cannot recall the details.) So the volume computation would be a lot more complicated than you've laid out.
My first though as well.
BUT corners and edges chip. A sphere is far more mechanically robust.