Problem $2.$ Longer problem focused on problem solving multiple steps. This problem will be graded based on process, clarity of work, and correct answer and units.

The shape below has dimensions of $a=3\mathrm{.}9in.,b=7\mathrm{.}3in.,$ and $c=4\mathrm{.}3in.$

a$.$ What is the value of $I_{\text{m}\text{i}\text{n}}$ and $I_{\text{m}\text{a}\text{x}}$ as well as the orientation of the principal centroidal axes $($strong and weak axes$)$ for the shape shown?