1. The problem is to find the radius $r$ of a circle given its area $A = 25$ cm² and the formula for the area of a circle $A = \pi r^2$. 2. The formula for the area of a circle is: $$A = \pi r^2$$ where $A$ is the area and $r$ is the radius. 3. Substitute the given area into the formula: $$25 = \pi r^2$$ 4. Solve for $r^2$ by dividing both sides by $\pi$: $$r^2 = \frac{25}{\pi}$$ 5. Show the division with cancellation notation: $$r^2 = \frac{25}{\cancel{\pi}}$$ 6. Take the square root of both sides to find $r$: $$r = \sqrt{\frac{25}{\pi}}$$ 7. Simplify the square root: $$r = \frac{\sqrt{25}}{\sqrt{\pi}} = \frac{5}{\sqrt{\pi}}$$ 8. This is the exact radius. For an approximate decimal value, use $\pi \approx 3.1416$: $$r \approx \frac{5}{1.772} \approx 2.82 \text{ cm}$$ Final answer: The radius $r$ is approximately $2.82$ cm.