## Physics Technology Update (4th Edition)

No, It is not possible to determine whether the area of the circle is $\pi r ^{2}$ or 2 $\pi r ^{2}$
Dimensional analysis is used to check the dimensional consistency of the physical equation. However, only the physical quantities that have dimension can be checked. There is no way to check dimensionless factors like numbers. In this case, the dimensions of both the equations is the same as that of the area, but there is no way to check whether it is $\pi r ^{2}$ or 2 $\pi r ^{2}$ because 1 and 2 are dimensionless. Both the equations are dimensionally correct.