In Bragg's approach to the determination of the Avogadro constant, the measurement of silicon density as the ratio of mass to volume is an essential step. With a view to achieving a relative uncertainty of 10(-7) in the determination of N(A), the computation of the volumes of solid density standards manufactured in the form of optically-polished silicon balls was investigated. Apart from a negligible difference, the volume considered is that of a sphere having the same average diameter. The estimation of the average diameter is studied in the angular momentum domain by using spherical harmonics as a basis and results are assessed by Monte Carlo simulation. The N-point approximation is investigated in detail and a formula for the uncertainty and sampling which minimize aliasing is also given. If the spectrum is bandwidth limited, it is demonstrated that N-point means exist, which give the average diameter exactly. The work involves least-squares estimation and refers to discrete Fourier transforms, Nyquist sampling criterion and analogies with quantum mechanical formulae.