Assume that an object covers an area A and has a uniform height h. If its cross-sectional area is uniform over its height, then its volume is given by V = Ah.
(a) Show that
V = Ah is dimensionally correct.
(b) Show that the volumes of a cylinder and of a rectangular box can be written in the form V = Ah, identifying A in each case. (Note that
A, sometimes called the “footprint” of the object, can have any shape and the height can be replaced by average thickness in general.)