Answer
The ratio is 2:1.
Work Step by Step
For the square circumscribed about the circle, the length of a side is equal to the diameter of the circle. Therefore, A=d$^2$. For the square inscribed in the circle, the diameter of the circle is equal to the diameter of the square. Therefore, a side of the square is equal to $\frac{d\sqrt 2}{2}$. With this information we know that the area, a, of the inscribed circle is $\frac{d^2}{2}$.
Ratio=$\frac{A}{a}$
R=$\frac{d^2}{\frac{d^2}{2}}$
R=$\frac{2d^2}{d^2}$
R=2
