If a $$ 120^{\circ} $$ sector of a circle has radius 18 cm , what is the perimeter of the sector? The perimeter of the sector is (Simplify your answer. Type an exact answer, using $$ \pi $$ as needed.)

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1. The perimeter of the sector consists of the arc length plus the lengths of the two radii.

2. First, convert the central angle from degrees to radians. Since the central angle is $$ 120^{\circ} $$, we have:
   $$
   120^{\circ} = 120 \times \frac{\pi}{180} = \frac{2\pi}{3} \text{ radians.}
   $$

3. The arc length $$ s $$ of a circle is given by:
   $$
   s = R\theta,
   $$
   where $$ R = 18 $$ cm and $$ \theta = \frac{2\pi}{3} $$. Therefore:
   $$
   s = 18 \times \frac{2\pi}{3} = 12\pi \text{ cm.}
   $$

4. The perimeter $$ P $$ of the sector is the sum of the arc length and the two radii:
   $$
   P = 12\pi + 18 + 18 = 12\pi + 36 \text{ cm.}
   $$

5. Thus, the exact perimeter of the sector is:
   $$
   12\pi + 36.
   $$
The perimeter of the sector is $$ 12\pi + 36 $$ cm.

If a sector of a circle has radius 18 cm , what is the perimeter of the sector?
The perimeter of the sector is
(Simplify your answer. Type an exact answer, using as needed.)

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If a sector of a circle has radius 18 cm , what is the perimeter of the sector? The perimeter of the sector is (Simplify your answer. Type an exact answer, using as needed.)