Consider a $5$ cm x $1$ cm x $1$cm bar of aluminum. When a compressive load of $500$ kN is

applied along the $5$ cm axis, the bar is compacted to a length of $4\mathrm{.}637$ cm$.$

a$)$ Calculate the axial strain and transverse strain experienced by the bar if Poisson$$s ratio

for aluminum is $0\mathrm{.}334.$

b$)$ What is the resulting with of the sample $($in cm$)$ after the force has been applied?