1. **State the problem:** We need to find the volume of a pentagonal prism with a height of 13 cm, each side of the pentagonal base measuring 13 cm, and the apothem (distance from the center to a side) of the pentagon is 8 cm. 2. **Formula for volume of a prism:** $$V = B \times h$$ where $B$ is the area of the base and $h$ is the height of the prism. 3. **Calculate the area of the pentagonal base:** The area of a regular pentagon is given by: $$B = \frac{1}{2} \times P \times a$$ where $P$ is the perimeter and $a$ is the apothem. 4. **Calculate the perimeter $P$:** Since each side is 13 cm and there are 5 sides, $$P = 5 \times 13 = 65 \text{ cm}$$ 5. **Calculate the base area $B$:** $$B = \frac{1}{2} \times 65 \times 8 = \frac{1}{2} \times 520 = 260 \text{ cm}^2$$ 6. **Calculate the volume $V$:** Using the height $h = 13$ cm, $$V = 260 \times 13 = 3380 \text{ cm}^3$$ 7. **Conclusion:** The volume of the pentagonal prism is $3380$ cubic centimeters. **Final answer:** C) 3380 cm³