Question

A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying outside the circle and inside the square .

Answer 1

DISCLAIMER: There is some error in the given question.
We have solved the question by taking a square inscribed in a circle. Then finding the area inside the circle and outside the square.


Diagonal of the square = 8 cm.
Let the side of the square be a cm.
In triangle BCD,
$$\begin{gathered} B{C}^2+C{D}^2=B{D}^2 \\ \Rightarrow a^2+a^2=8^2 \\ \Rightarrow a^2=32.....\left(\mathrm{i}\right) \end{gathered}$$
Radius of the circle will be R = 4 cm
Now area between the circle and the square will be
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{circle}-\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square} \\ =\mathrm{\pi }{\left(R\right)}^2-a^2 \\ =\mathrm{\pi }{\left(4\right)}^2-32 \\ =\left(16\mathrm{\pi }-32\right){\mathrm{cm}}^2 \end{gathered}$$