Answer:
Maxwell's method is useful.
Actually, the way Maxwell is attempting to determine the volume is not wrong, according to Archimede's principle. Maxwell's method will measure the weight of the displaced water, which will be useful to determin the volume, because he already know the density of the water.
It would be better if he uses a heavier object to have a greater water displacement. Specifically, the Archimede's principle states:
Weight of displaced fluid = weight of the object (pennies) - weight of the object in fluid.