$$ 1 \leftarrow \quad $$ A $$ 22-\mathrm{m} $$ wire is wrapped around a circular region. If the wire fits exactly, what is the area of the region? The area of the region is (Type an exact answer in terms of $$ \pi $$.)

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We start with the circumference of the circle given by the length of the wire:

$$
C = 22 = 2\pi r
$$

Solve for the radius $$ r $$:

$$
r = \frac{22}{2\pi} = \frac{11}{\pi}
$$

Now, the area $$ A $$ of a circle is given by:

$$
A = \pi r^2
$$

Substitute the value of $$ r $$:

$$
A = \pi \left(\frac{11}{\pi}\right)^2 = \pi \cdot \frac{121}{\pi^2} = \frac{121}{\pi}
$$

Thus, the area of the region is:

$$
\frac{121}{\pi}
$$
The area of the region is $$ \frac{121}{\pi} $$.

A wire is wrapped around a circular region. If the wire fits exactly, what is the area of the region?
The area of the region is
(Type an exact answer in terms of .)

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A wire is wrapped around a circular region. If the wire fits exactly, what is the area of the region? The area of the region is (Type an exact answer in terms of .)