1. The problem states that the area of a circle is given as 20 and the diameter is given as 10, which implies the radius $r$ is 5 because $r = \frac{diameter}{2} = \frac{10}{2} = 5$. 2. The formula for the area of a circle is $A = \pi r^2$. 3. Substitute the radius $r=5$ into the formula: $$A = \pi \times 5^2 = 25\pi.$$ 4. Calculate $25\pi$ approximately: $$25 \times 3.1416 = 78.54$$. 5. The area from calculation is approximately 78.54, but the problem states the area as 20, so there might be a discrepancy or misunderstanding in the problem statement. 6. If the area is confirmed to be 20, then to find the radius from this area, we use $A = \pi r^2$ and solve for $r$: $$r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{20}{3.1416}} \approx 2.52.$$ 7. This radius value $2.52$ conflicts with the radius $5$ derived from the given diameter 10. Please check the problem parameters.