**Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2? Explain.**

**Answer:**

The dimensional formula for area a is given as follows:

Here, L is dimension of length.

The factor 2 is a constant, and it is dimensionless.

That is dimension of area. When dimension is correct, dimension analysis cannot tell whether a constant like 2 should be there or not.

Thus, the dimensional analysis **can not** determine whether the area of a circle is πr2 or 2πr2 because the factor 2 is dimensionless.