Consider a bar$-$shaped sample of aluminum oxide having a square cross section of $1$cm x $1$cm$,$ and length $8$cm$.$ The bulk density of this sample was measured to be $3\mathrm{.}60$ g$/$cm$3.$ The theoretical density of Al$2$O$3$ is $3\mathrm{.}98$g$/$cm$3.$ For fully dense alumina, the elastic modulus is $400$ GPa, and the average modulus of rupture $($MOR$)$ is $420$ MPa. You know the following equations