$($A$)$ Verify that the maximum void ratio and porosity of the idealized sandy soil, in its loosest state, are indeed $0\mathrm{.}91$ and $0\mathrm{.}476(47\mathrm{.}6\%),$ respectively. A single solid particle with radius R would fit a cubical unit volume with dimensions $2R2R2R(8R^3).($Show all pertinent volume$-$weight relationships and calculations.$)$