Lagrange multipliers and uncommon question

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Suppose you have $n$ cobblestone blocks of dimensions $a, b$, and $c$ to build a water tank.

(a) What is the tank shape that maximizes volume? Cube, cylinder ...

(b) Determine an expression for this volume.

The exercises I have come across to this day have always said the shape of the object for volume optimization. How do I follow the reverse path? Should I list the format possibilities?