Question: A circular piece of paper has a radius of $13$ cm.
A circular hole with a radius of $5$ cm is cut in the centre of the piece of paper to make the shape below.
Calculate the area of this shape.
Give your answer to 1 d.p.
Shape: annulus (ring) with outer radius $13$ cm and inner radius $5$ cm, position_hint=center.
1. **State the problem:** We need to find the area of an annulus (ring-shaped figure) formed by cutting a smaller circle of radius $5$ cm from the center of a larger circle of radius $13$ cm.
2. **Formula:** The area of an annulus is given by the difference between the area of the larger circle and the smaller circle:
$$\text{Area} = \pi R^2 - \pi r^2 = \pi (R^2 - r^2)$$
where $R$ is the outer radius and $r$ is the inner radius.
3. **Substitute values:**
$$\text{Area} = \pi (13^2 - 5^2) = \pi (169 - 25) = \pi \times 144$$
4. **Calculate:**
$$\text{Area} = 144\pi$$
Using $\pi \approx 3.1416$:
$$\text{Area} \approx 144 \times 3.1416 = 452.389$$
5. **Round to 1 decimal place:**
$$\text{Area} \approx 452.4 \text{ cm}^2$$
**Final answer:** The area of the annulus is approximately $452.4$ cm$^2$.