Engineering vs$.$ true stress and strain: A $5$ inch long aluminum rod with a diameter of $0\mathrm{.}5$ inch is subjected to a tensile force of $3000$ lbf $.$ If the diameter decreases to $0\mathrm{.}45$ inch and assume the volume of the rod remains constant, calculate:

$($a$)$ The engineering stress and strain at this load. $(2$ points$)$

$($b$)$ The true stress and strain at this load. $(2$ points$)$