Answer
$64 \pi \ cm^2$
Work Step by Step
Let $A$ be the area of a sector of a circle . The area $(A)$ of a sector of a circle whose radius is $r$ is given by: $A=\pi r^2 \times \dfrac{Measure \ of \ the \ arc}{360^{\circ}}...(1)$
We are given that radius $r=16 \ cm$ and $Measure \ of \ the \ arc=90^{\circ}$
Plug the data in the equation (1) to obtain:
$A=\pi (16^2 \times \dfrac{90^{\circ}}{360^{\circ}}=64 \pi \ cm^2$
Therefore, we get , $Area=64 \pi \ cm^2$
