1. **State the problem:** Find the volume of a cone with radius $r=5$ cm and height $h=8$ cm. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ This formula calculates the volume by taking one-third of the base area times the height. 3. **Substitute the given values:** $$V = \frac{1}{3} \pi (5)^2 (8)$$ 4. **Calculate the square of the radius:** $$5^2 = 25$$ 5. **Plug in and simplify:** $$V = \frac{1}{3} \pi \times 25 \times 8$$ 6. **Multiply 25 and 8:** $$V = \frac{1}{3} \pi \times 200$$ 7. **Simplify the fraction:** $$V = \cancel{\frac{1}{3}} \pi \times \cancel{200} \times \frac{200}{3} \pi$$ 8. **Calculate the volume numerically:** $$V = \frac{200}{3} \times 3.1416 \approx 209.44$$ 9. **Round to the nearest tenth:** $$V \approx 209.4$$ cubic centimeters. **Final answer:** The volume of the cone is about 209.4 cubic centimeters.