Answer
$56 \pi \ cm^2$
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 know that the radius id half of the diameter of a circle. That is, $r=\dfrac{d}{2}=\dfrac{16}{2}=8 \ cm$
$Measure \ of \ the \ arc=360^{\circ}-45^{\circ}=315^{\circ}$
Plug the data in the equation (1) to obtain:
$A=\pi (8)^2 \times \dfrac{315^{\circ}}{360^{\circ}}$
Therefore, we get , $Area=56 \pi \ cm^2$
