Explanation:

Write the dimensional formula for the area of the circle πr2 .

πr2=[L0][L2]=[L2] (1)

Here,

L is the dimension of the length.

Write the dimensional formula for the area of the circle 2πr2 .

2πr2=[L0][L0][L2]=[L2] (2)

Here,

L is the dimension of the length.

From the equation (1) and (2) the dimension of the area is same in both cases. So that the dimensional analysis cannot be determine whether the area of a circle is πr2 or 2πr2 .

The dimensions of the variable do not depend on the numeric number.

Conclusion:

Therefore, the dimensional analysis cannot determine whether the area of a circle is πr2 or 2πr2 .