1. **State the problem:** We need to find the volume of a shape made by combining a cone and a hemisphere. The hemisphere has radius $r=7$ cm, and the cone has radius $r=7$ cm and height $h=12$ 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:** $$V_{hemisphere} = \frac{2}{3} \pi (7)^3 = \frac{2}{3} \pi \times 343 = \frac{686}{3} \pi$$ 4. **Calculate the volume of the cone:** $$V_{cone} = \frac{1}{3} \pi (7)^2 \times 12 = \frac{1}{3} \pi \times 49 \times 12 = \frac{1}{3} \pi \times 588 = 196 \pi$$ 5. **Add the volumes to get total volume:** $$V_{total} = V_{hemisphere} + V_{cone} = \frac{686}{3} \pi + 196 \pi = \left(\frac{686}{3} + 196\right) \pi = \left(\frac{686}{3} + \frac{588}{3}\right) \pi = \frac{1274}{3} \pi$$ 6. **Calculate numerical value:** $$V_{total} \approx \frac{1274}{3} \times 3.1416 = 424.6667 \times 3.1416 \approx 1333.33$$ 7. **Final answer rounded to nearest integer:** $$\boxed{1333}$$ cubic centimeters. This is the volume of the combined shape made from the cone and hemisphere.