In the Densest Molecular Clouds, the Average Density Is Approximately $\odot$

Essay

In the densest molecular clouds, the average density is approximately 300 atoms/cm³. If a cube of molecular cloud gas with this density contained 100 M _$\odot$ of material (the amount needed to make a 1 M _$\odot$ star), what would be the length of a side of the cube in units of AU? For reference, the mass of the Sun is 2 * 10³⁰ kg, the mass of a hydrogen atom is 1.7 *10 ^{- 27} kg, and 1 AU = 1.5 * 10¹¹ m.