To find the area of a circle when the radius is given, you can use the formula for the area of a circle:
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius.
From the information given, we see that a circle with a radius of 2 inches has an area of 12.568 square inches. Let's check this calculation based on the area formula:
\[ A = \pi (2^2) = \pi (4) \approx 12.566 \text{ square inches} \]
The given area is approximately equal to \( \pi \) (which is about 3.14159); thus the calculation seems consistent.
Now we will find the area for a circle with radius 6.2 inches:
\[ A = \pi (6.2^2) = \pi (38.44) \]
Now, calculate \( \pi \times 38.44 \):
\[ A \approx 3.14159 \times 38.44 \approx 120.655 \]
Rounding to the nearest thousandths, we have:
\[ A \approx 120.655 \text{ in. squared} \]
Thus, the area of a circle with a radius of 6.2 inches is approximately 120.655 in².