Answer :
Answer:
To find the area of the shaded region between two concentric circles, we need to subtract the area of the smaller circle from the area of the larger circle.
Given:
- Radius of the larger circle (\( R \)) = 11 cm
- Radius of the smaller circle (\( r \)) = 9 cm
First, calculate the area of each circle using the formula \( \pi r^2 \):
Area of the larger circle:
\[ A_{\text{larger}} = \pi \times (11)^2 = 121 \pi \text{ square cm} \]
Area of the smaller circle:
\[ A_{\text{smaller}} = \pi \times (9)^2 = 81 \pi \text{ square cm} \]
Now, find the area of the shaded region, which is the difference between the area of the larger circle and the area of the smaller circle:
\[ \text{Area of shaded region} = A_{\text{larger}} - A_{\text{smaller}} \]
\[ \text{Area of shaded region} = 121 \pi - 81 \pi \]
\[ \text{Area of shaded region} = 40 \pi \]
Therefore, the area of the shaded region is \( \boxed{40 \pi} \) square centimeters.