A drop of water of radius 1 mm is broken into 1000 droplets of equal size. The ratio of total surface area after : before equals:

**Volume conservation:** $\frac{4}{3}\pi R^3 = 1000 \cdot \frac{4}{3}\pi r^3$ ⇒ $r = R/10$. **Surface area before:** $4\pi R^2$. **After:** $1000 \times 4\pi r^2 = 1000 \times 4\pi R^2/100 = 10 \times 4\pi R^2$. Ratio = 10:1 — surface area grows 10×, requiring 9× work against surface tension.