1. **State the problem:** We need to find the volume of a pentagonal prism where each side of the pentagonal base is 8 inches and the height of the prism is 5.5 inches. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Height}$$ 3. **Find the area of the pentagonal base:** The pentagon is regular with side length $s = 8$ inches. The formula for the area of a regular pentagon is: $$\text{Area} = \frac{1}{4} \sqrt{5(5+2\sqrt{5})} s^2$$ 4. **Calculate the base area:** $$\text{Area} = \frac{1}{4} \sqrt{5(5+2\sqrt{5})} \times 8^2 = \frac{1}{4} \sqrt{5(5+2\sqrt{5})} \times 64$$ 5. **Simplify the expression:** Calculate inside the square root: $$5 + 2\sqrt{5} \approx 5 + 2 \times 2.236 = 5 + 4.472 = 9.472$$ Then: $$\sqrt{5 \times 9.472} = \sqrt{47.36} \approx 6.883$$ So, $$\text{Area} \approx \frac{1}{4} \times 6.883 \times 64 = \frac{1}{4} \times 440.512 = 110.128$$ 6. **Calculate the volume:** $$\text{Volume} = \text{Base Area} \times \text{Height} = 110.128 \times 5.5 = 605.704$$ 7. **Final answer:** The volume of the pentagonal prism is approximately $$\boxed{605.7 \text{ cubic inches}}$$