Question: The area of this circle is $83$ cm$^2$
Calculate the radius of this circle to $1$ d.p.
1. **State the problem:** We are given the area of a circle as $83$ cm$^2$ and need to find its radius rounded to $1$ decimal place.
2. **Formula:** The area $A$ of a circle is given by the formula:
$$A = \pi r^2$$
where $r$ is the radius.
3. **Rearrange the formula to solve for $r$:**
$$r^2 = \frac{A}{\pi}$$
$$r = \sqrt{\frac{A}{\pi}}$$
4. **Substitute the given area:**
$$r = \sqrt{\frac{83}{\pi}}$$
5. **Calculate the value inside the square root:**
$$\frac{83}{\pi} \approx \frac{83}{3.1416} \approx 26.42$$
6. **Take the square root:**
$$r = \sqrt{26.42} \approx 5.14$$
7. **Round to 1 decimal place:**
$$r \approx 5.1$$
**Final answer:** The radius of the circle is approximately $5.1$ cm.