Solving the knapsack problem for practical instances is actually really easy. (That's a general pattern with NP hard problem: most of them are easy in practice.)

But the problem described is closer to two- or three-dimensional bin packing (or scheduling in general) than to the knapsack problem. See eg http://www.research.ibm.com/people/n/nikhil/papers/Bansal-pa...

Another thing to look at is the "Cutting stock" problem (https://en.wikipedia.org/wiki/Cutting_stock_problem).

Knapsack is only about weight, while this is about (most likely) packing 3D cuboids. But that problem is NP-hard, too ;)