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27 spherical drops of a liquid are merged to form a single large spherical drop. If the radius of the smaller drop is $$1\text{ mm}$$, find the radius of the larger drop. Also find the ratio surface area of the larger drop to the total surface area of all the drops.
Correct Answer: 0
PLACEHOLDER ANSWER - the question has two answers. Volume is conserved, so $$R^3 = 27r^3$$ and $$R = 3\text{ mm}$$. The large drop has area $$4\pi(3)^2 = 36\pi$$ and the 27 small drops have total area $$27 \times 4\pi = 108\pi$$. So the ratio is $$1 \colon 3$$.
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