To calculate the area of the shape, we need to find the area of the larger circle and subtract the area of the smaller circle.

Step 1: Formula for the area of a circle

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

Step 2: Area of the larger circle

The radius of the larger circle is $11 \, \text{cm}$. $A_{\text{larger}} = \pi (11)^2 = 121\pi$ Using $\pi \approx 3.1416$: $A_{\text{larger}} = 121 \times 3.1416 \approx 380.1 \, \text{cm}^2$

Step 3: Area of the smaller circle

The radius of the smaller circle is $5 \, \text{cm}$. $A_{\text{smaller}} = \pi (5)^2 = 25\pi$ Using $\pi \approx 3.1416$: $A_{\text{smaller}} = 25 \times 3.1416 \approx 78.5 \, \text{cm}^2$

Step 4: Area of the remaining shape

To find the area of the remaining shape, subtract the area of the smaller circle from the area of the larger circle: $A_{\text{remaining}} = A_{\text{larger}} - A_{\text{smaller}}$ $A_{\text{remaining}} = 380.1 - 78.5 = 301.6 \, \text{cm}^2$

Final Answer:

The area of the shape is: $\boxed{301.6 \, \text{cm}^2}$

Would you like further clarifications or detailed steps?

Here are 5 related questions to deepen understanding:

1. How would the area change if the smaller circle's radius was 6 cm instead of 5 cm?
2. How do you calculate the circumference of the resulting shape?
3. What would the area of the shape be in terms of $\pi$ instead of decimals?
4. How can this problem be adapted for a different geometric shape (e.g., a square hole instead of a circular one)?
5. What practical situations could require this kind of calculation?

Tip: Always double-check units and ensure you use the same value of $\pi$ consistently throughout the calculations!