Molten Sphere Surface Area Increase

Large sphere volume = $\frac{4}{3}\pi R^3 = \frac{4}{3}\pi (10^3)$. Small spheres radius $r$: $1000 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (10^3) \implies r = 1$ cm. Original surface area = $4\pi (10^2) = 400\pi$. Total new surface area = $1000 \times 4\pi (1^2) = 4000\pi$. Increase in surface area = $4000\pi - 400\pi = 3600\pi$, which is an increase of 9 times (or 10 times the original value, increased by 900%). Neither 1000, 100, 10, nor no change is correct. Hence, None of the above.