Answer :

We are given the radius of a circle as
[tex]$$
r = 38.6.
$$[/tex]

The formula for the area of a circle is
[tex]$$
A = \pi r^2.
$$[/tex]

Step 1. Square the radius:
Substitute the value of [tex]$r$[/tex] into the expression:
[tex]$$
r^2 = (38.6)^2 \approx 1489.96.
$$[/tex]

Step 2. Multiply by [tex]$\pi$[/tex]:
Now, plug [tex]$1489.96$[/tex] into the area formula:
[tex]$$
A = \pi \times 1489.96 \approx 4680.847390142649.
$$[/tex]

Step 3. Round the area:
Rounding to the nearest hundredth, we have:
[tex]$$
A \approx 4680.85.
$$[/tex]

Therefore, the area of the circle is
[tex]$$
\boxed{4680.85}.
$$[/tex]