Q$1$: $(25$ pts$)$

A cylindrical rod with a cross$-$sectional area of A loaded in tension with an axial force of $P=8900N$ undergoes a stress of $=\frac{P}{A}.$

a$)$ Using a material strength of $165$ MPa and a design factor of $3\mathrm{.}0,$ determine the minimum diameter of a solid circular rod.

b$)$ Using the table below, select a suitable standard diameter for the calculated value and determine the rod's factor of safety.

$\backslash$table$[[$Standard diameter for solid circular rod $[$mm$]],[9,0,10,0,11,0,12,0,14\mathrm{.}0,16,0,18\mathrm{.}0,20\mathrm{.}0,22\mathrm{.}0,25,0,28,0,30\mathrm{.}0,32\mathrm{.}0]]$