Answer
The rate at which the minute hand sweeps out area is $\frac{\pi~r^2}{3600}~cm^2/s$
Work Step by Step
Let $r$ be the length of the minute hand. Then the total area swept out by the minute hand is $A = \pi~r^2$
The minute hand sweeps out this area in one hour, which is 3600 seconds.
The rate at which the minute hand sweeps out area is:
$\frac{dA}{dt} = \frac{\pi~r^2}{3600}~cm^2/s$