How does the volume of a cube change if the length of one side is increased by one unit, another side is decreased by one unit, and the third side is left unchanged? How does changing the shape of a container affect the volume of the matter?

Answer 1

The volume of a^3 (where a is a side length of the original cube) becomes
a*(a+1)(a-1) = a*(a^2 -1) = a^3 - a^2
, which is less than the original volume.

The fractional decrease in volume depends upon what the "units" of length are.