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 (which represents the hole cut in the paper).

1. Area of the larger circle:
   The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius.

   • For the larger circle, the radius is $15 \, \text{cm}$: $A_{\text{large}} = \pi (15)^2 = 225\pi \, \text{cm}^2$

2. Area of the smaller circle (the hole):

   • For the smaller circle, the radius is $4 \, \text{cm}$: $A_{\text{small}} = \pi (4)^2 = 16\pi \, \text{cm}^2$

3. Subtract the area of the smaller circle from the area of the larger circle: $A_{\text{shape}} = A_{\text{large}} - A_{\text{small}} = 225\pi - 16\pi = 209\pi \, \text{cm}^2$

4. Calculate the numerical value: Using $\pi \approx 3.1416$: $A_{\text{shape}} \approx 209 \times 3.1416 = 656.6 \, \text{cm}^2$

Therefore, the area of the shape is approximately 656.6 cm² (to 1 decimal place).

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. What would the area be if the smaller circle had a radius of 6 cm?
2. How does the shape change if the hole is not centered?
3. How can we calculate the circumference of the outer circle?
4. What is the ratio of the area of the hole to the total area of the paper?
5. How would the area change if we scaled the radius of both circles by 50%?

Tip: The difference of areas between two concentric circles forms an annular ring, and you can generalize the formula as $\pi (R^2 - r^2)$ for quick calculations.