A solid metal sphere of radius 15 cm is melted and recast into 27 identical smaller spheres. What is the ratio of the surface area of the original sphere to the total surface area of all 27 smaller spheres?

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Accepted Answer

1. Use volumes. Original volume = $\frac{4}{3}\pi(15)^3$. Each small sphere has volume = original/27, so $r^3=15^3/27$ and $r=15/3=5$ cm.

2. Find areas. Original area = $4\pi(15)^2=900\pi$. Each small area = $4\pi(5)^2=100\pi$.

3. Total small area = $27	imes100\pi=2700\pi$. Ratio original : total = $900\pi:2700\pi=1:3$.

FINAL_ANSWER: a

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