The diameter of the circle is the same as the side length of the bounding square. The radius of the circle is 8 in, so the side length of the square is 16 in.
Then the area between the square and circle is obtained by subtracting the area of the circle from the area of the square:
[tex]A_{\rm circle}=\pi(8\,\mathrm{in})^2=64\pi\,\mathrm{in}^2[/tex]
[tex]A_{\rm square}=(16\,\mathrm {in})^2=256\,\mathrm{in}^2[/tex]
and the area you want is
[tex]256-64\pi\,\mathrm{in}^2\approx54.9\,\mathrm{in}^2[/tex]
