Answer
(32$\pi$ - 64)$in^{2}$
Work Step by Step
In the circle diameter of the circle = diagonal of the square
By pythagoras theorem
$diagonal^{2}$ = $8^{2}$ + $8^{2}$
$diagonal^{2}$ = 64 + 64
diagonal = $\sqrt 128 $ = 8$\sqrt 2$ in
Therefore the diameter of the circle = 8$\sqrt 2$ in
Area of the circle = $\pi r^{2}$
= $\pi (4\sqrt 2)^{2}$ = 32$\pi in^{2}$
Area of square = $s^{2}$ = $8^{2}$ = 64 $in^{2}$
Therefore the shaded area = (32$\pi$ - 64)$in^{2}$
