1. **Problem:** Find the volume of a hemisphere with a great circle circumference of 37.7 centimeters. 2. **Formula:** The volume of a hemisphere is given by $$V = \frac{2}{3} \pi r^3$$ where $r$ is the radius of the hemisphere. 3. **Step 1: Find the radius from the circumference.** The circumference $C$ of a great circle is related to the radius by $$C = 2 \pi r$$ Given $C = 37.7$, solve for $r$: $$r = \frac{C}{2 \pi} = \frac{37.7}{2 \pi}$$ 4. **Calculate $r$: ** $$r = \frac{37.7}{2 \times 3.1416} = \frac{37.7}{6.2832} \approx 6.0$$ 5. **Step 2: Calculate the volume of the hemisphere.** $$V = \frac{2}{3} \pi r^3 = \frac{2}{3} \pi (6.0)^3$$ 6. **Calculate $r^3$: ** $$6.0^3 = 6.0 \times 6.0 \times 6.0 = 216$$ 7. **Calculate volume:** $$V = \frac{2}{3} \times 3.1416 \times 216 = \frac{2}{3} \times 678.58 = 452.39$$ 8. **Final answer:** The volume of the hemisphere is approximately **452.39 cubic centimeters**.