1. The problem asks for the formula to find the volume $V$ of a composite solid consisting of a hemisphere on top of a cone. 2. The volume of a hemisphere is given by the formula: $$V_{hemisphere} = \frac{2}{3} \pi r^3$$ where $r$ is the radius. 3. The volume of a cone is given by the formula: $$V_{cone} = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 4. Since the composite solid is the hemisphere on top of the cone, the total volume is the sum of the two volumes: $$V = V_{hemisphere} + V_{cone} = \frac{2}{3} \pi r^3 + \frac{1}{3} \pi r^2 h$$ 5. Comparing this with the options given: - Option A: $\frac{4}{3} \pi r^3 + \frac{1}{3} \pi r^2 h$ (incorrect hemisphere volume) - Option B: $\frac{2}{3} \pi r^3 + \frac{1}{3} \pi r^2 h$ (correct) - Option C: $\frac{2}{3} \pi r^3 + \frac{1}{2} \pi r^2 h$ (incorrect cone volume) - Option D: $\frac{4}{3} \pi r^3 + \frac{1}{2} \pi r^2 h$ (both incorrect) 6. Therefore, the correct formula is option B: $$V = \frac{2}{3} \pi r^3 + \frac{1}{3} \pi r^2 h$$