A square metal sheet (6 feet x 6 feet) is to be made into an
open-topped water tank by cutting squares from the four
corners of the sheet, and bending the four remaining
rectangular pieces up, to form the sides of the tank. These
edges will then be welded together.
A. How will the final volume of the tank depend upon the size of
the squares cut from the corners?
Describe your answer by:
i) Sketching a rough graph
ii) Explaining the shape of your graph in words
iii) Writing an algebraic formula for the volume

B. How large should the four corners be cut, so that the resulting volume of the tank is as large as possible?