If the diameter of a sphere is 6 m, its hemisphere will have a volume of

### Concept & Hemisphere Volume A hemisphere is exactly half of a sphere. Its volume is derived by halving the standard volume formula of a full sphere. $$V_{hemisphere} = \frac{1}{2} \times \left( \frac{4}{3}\pi r^3 \right) = \frac{2}{3}\pi r^3$$ ### Step-by-Step Solution 1. **Find Radius:** Given diameter $d = 6\text{ m}$. Radius $r = \frac{d}{2} = \frac{6}{2} = 3\text{ m}$. 2. **Calculate Hemisphere Volume:** $V = \frac{2}{3}\pi r^3$ $V = \frac{2}{3}\pi (3)^3$ $V = \frac{2}{3}\pi (27)$ $V = 2 \times 9\pi = 18\pi\text{ m}^3$ ### Exam Strategy & Shortcut Calculate the sphere's volume $\frac{4}{3}\pi (3^3) = 36\pi$, and immediately cut it in half to get $18\pi$. This prevents over-memorization of hemisphere-specific formulas. ### Common Pitfall Using the given diameter ($6\text{ m}$) directly in the formula instead of converting it to the radius ($3\text{ m}$), which would incorrectly lead to $144\pi$. ### Final Answer Therefore, the correct answer is **18\pi**.