$2$ Part $2$: Short Answer $(20$ Marks$)$

Answer the following questions in the space provided on this sheet.

The demon core, so named because of it's involvement in a number of criticality experiments during the manhattan project, was a $6\mathrm{.}2$ kg sphere of plutonium$-$gallium alloy measuring $89$ mm in diameter. It was assembled to be $-5$ cents $($slightly subcritical$).$ To keep those handling it safe, it might have been encased in a sphere with packing