To find the area of the shaded region, we need to calculate the area of the circle and subtract the area of the square inside it.

1. Calculate the area of the circle:

   • The radius of the circle is 3.0 cm.
   • Area of the circle $A_{\text{circle}} = \pi r^2$ $A_{\text{circle}} = \pi \times (3.0)^2 = 9\pi \approx 28.27 \text{cm}^2$

2. Calculate the area of the square:

   • The side length of the square is 6.0 cm.
   • Area of the square $A_{\text{square}} = s^2$ $A_{\text{square}} = 6.0^2 = 36.0 \text{cm}^2$

3. Find the area of the shaded region:

   • The shaded area is given by the area of the circle minus the area of the square. [ A_{\text{shaded}} = 28.27 \text{cm}^2 - 36.0 \text{cm}^2