The equation $A=4\pi r^2$ is dimensionally correct.
Work Step by Step
In the equation $A=4\pi r^2$, $A$ is area and has SI units $m^2$. On the other side, $\pi$ is a dimensionless constant; and, $r^2$ has SI units $m^2$. Both sides have the same SI units, and therefore, the equation is dimensionally correct.