   Chapter 1, Problem 3P

Chapter
Section
Textbook Problem

A shape that covers an area A and has a uniform height h has a volume 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 that the height can, in general, be replaced by the average thickness of the object.)

(a)

To determine
The correctness of the dimension of the volume equation V=Ah.

Explanation

The R.H.S of the equation is volume, It has a dimension of [L3]

The expression for the L.H.S is Ah

Substitute the dimension [L2] for [A] and [L] for [h]

(b)

To determine
The equality of the dimension of the volume of the cylinder and the rectangular box.

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