To calculate the area of the shape shown (a circular piece of paper with a smaller circular hole cut out), we need to:

1. Find the area of the larger circle (radius = 11 cm).
2. Find the area of the smaller circle (radius = 5 cm).
3. Subtract the area of the smaller circle from the area of the larger circle to get the area of the shape.

Step 1: Area of the larger circle

The formula for the area of a circle is: $A = \pi r^2$ For the larger circle, $r = 11 \, \text{cm}$: $A_{\text{large}} = \pi \times 11^2 = \pi \times 121 \approx 380.13 \, \text{cm}^2$

Step 2: Area of the smaller circle

For the smaller circle, $r = 5 \, \text{cm}$: $A_{\text{small}} = \pi \times 5^2 = \pi \times 25 \approx 78.54 \, \text{cm}^2$

Step 3: Subtract the areas

Now subtract the area of the smaller circle from the area of the larger circle: $\text{Area of the shape} = 380.13 - 78.54 = 301.59 \, \text{cm}^2$

Final Answer

The area of the shape is approximately 301.6 cm² (rounded to 1 decimal place).

Do you want further details or have any questions?

Here are 5 related questions:

1. What would be the area if the radius of the hole was 7 cm instead?
2. How does changing the radius of the larger circle affect the final area?
3. How can you calculate the circumference of both circles?
4. What is the relationship between the area and the radius in a circle?
5. Can you calculate the area of a sector of the larger circle if part of it was cut out?

Tip: Always remember to subtract the area of the smaller circle from the larger one when dealing with ring-like shapes (annuli).