The Engineering Method and Problem Solving

The following problem is to be solved by hand, using either graphing or calculus techniques. You must organize and label your work according to the Engineering Method:

Recognize and understand the problem

Accumulate data and verify accuracy

Select appropriate theory or principle

Make necessary assumptions

Solve the problem $($use Calculus$)$

Verify and check results $($use EXCEL to create a proper graph$)$

In order to get credit, all six steps must be clearly labeled.

Problem: A cylindrical pressure vessel is constructed with AL$-6$XN stainless steel alloy metal for cryogenic storage capacity. The main body of the pressure vessel takes the shape of a cylinder with radius $r$ and height $h.$ For the pressure vessel to be installed properly at the industrial site, the pressure vessel dimensions must satisfy the requirement that the sum of the height plus ten times the radius should equal $60[m].$

What dimensions of $r$ and $h$ produce a pressure vessel with the largest volume storage capacity?