1. **State the problem:** We need to find the volume of a composite shape made of a cone and a hemisphere. The cone has height $h=15$ cm and radius $r=7$ cm. The hemisphere has radius $r=7$ cm. 2. **Formulas:** - Volume of a sphere: $$V_{sphere} = \frac{4}{3} \pi r^3$$ - Volume of a hemisphere: $$V_{hemisphere} = \frac{1}{2} V_{sphere} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3$$ - Volume of a cone: $$V_{cone} = \frac{1}{3} \pi r^2 h$$ 3. **Calculate the volume of the hemisphere:** $$V_{hemisphere} = \frac{2}{3} \pi (7)^3 = \frac{2}{3} \pi 343 = \frac{686}{3} \pi$$ 4. **Calculate the volume of the cone:** $$V_{cone} = \frac{1}{3} \pi (7)^2 (15) = \frac{1}{3} \pi 49 \times 15 = \frac{1}{3} \pi 735 = 245 \pi$$ 5. **Add the volumes to get total volume:** $$V_{total} = V_{cone} + V_{hemisphere} = 245 \pi + \frac{686}{3} \pi = \pi \left(245 + \frac{686}{3}\right) = \pi \left(\frac{735}{3} + \frac{686}{3}\right) = \pi \frac{1421}{3}$$ 6. **Calculate the numerical value:** $$V_{total} = \frac{1421}{3} \pi \approx 473.6667 \times 3.1416 \approx 1487.4$$ 7. **Round to nearest integer:** $$\boxed{1487}$$ The volume of the composite shape is approximately 1487 cubic centimeters.