$(30$ pts$)$ Problem $3$:

A floor joist which measures a full $2$ in $.$ by $8$ in $.$ has a $1-in.$ hole drilled through it for a waterpipe installation. Determine the percent reduction in the moment of inertia of the cross$-$sectional area about the x $-$axis $($compared with that of the undrilled joist$).$

$($Hint: You need to find the location of N$.$A$.$ of the drilled section first and then its moment of inertia around the new N$.$A$.$ compare with moment of inertia of the full $2$ in$.$ by $8$ in floor joist$).$