Answer
${\pi}r^{2}$ $cm^{2}/h$
Work Step by Step
the area $A$ of a sector of a circle with radius $r$ and angle $θ$ is given by
$A$ = $\frac{1}{2}r^{2}θ$
her e$r$ is constant and $θ$ varies so
$\frac{dA}{dt}$ = $\frac{1}{2}r^{2}\frac{dθ}{dt}$
the minute hand rotates through 360° = $2\pi$ radians each hour
$\frac{dA}{dt}$ = $\frac{1}{2}r^{2}(2\pi)$
$\frac{dA}{dt}$ = ${\pi}r^{2}$ $cm^{2}/h$
