A more precise, unit-respecting result is to plot the ratio of the unit sphere's volume to the unit cube's volume. This is a dimensionless quantity, so it makes

A more precise, unit-respecting result is to plot the ratio of the unit sphere's volume to the unit cube's volume. This is a dimensionless quantity, so it makes sense to compare them, but happily the numeric values are unchanged because the unit cube always has volume 1 m^N in dimension N.