To solve the problem of finding the area of the shaded region, we need to calculate the difference between the areas of the larger circle and the smaller circle.

Step 1: Formula for the area of a circle

The area of a circle is given by the formula: $A = \pi r^2$ where $r$ is the radius of the circle.

Step 2: Calculate the area of the larger circle

The radius of the larger circle is $11 \, \text{cm}$. Using the formula: $A_{\text{large}} = \pi (11)^2 = \pi (121) \approx 380.13 \, \text{cm}^2$

Step 3: Calculate the area of the smaller circle

The radius of the smaller circle is $3 \, \text{cm}$. Using the formula: $A_{\text{small}} = \pi (3)^2 = \pi (9) \approx 28.27 \, \text{cm}^2$

Step 4: Calculate the area of the shaded region

The shaded region is the difference between the larger and smaller circles: $A_{\text{shaded}} = A_{\text{large}} - A_{\text{small}} = 380.13 - 28.27 = 351.86 \, \text{cm}^2$

Final Answer:

The area of the shaded region is approximately: $\boxed{351.86 \, \text{cm}^2}$

Do you want a step-by-step diagram or further clarifications?

Related Questions:

1. What is the ratio of the areas of the smaller circle to the larger circle?
2. How would the result change if the radius of the larger circle increased by 2 cm?
3. Can you calculate the area of the ring-like region if the smaller circle is removed completely?
4. How does the difference in radii affect the area of the shaded region?
5. What is the circumference of each circle?

Tip:

Remember to always double-check units and rounding when performing area calculations!