(Solved):   The diagram of a rectangular prism with a square base is given below. Assume that the surf ...

 

The diagram of a rectangular prism with a square base is given below. Assume that the surface area of the prism is fixed at \( 216 \mathrm{~m}^{2} \). Find the width and height of the prism that will maximize its volume. The surface area of the prism \( =2(\text { width })^{2}+4 \) width height \( . \)