The surface areas of two spheres are in the ratio 1: 4. What is the ratio of their volumes?

Explanation

The ratio of surface areas is \frac{4\pi r_1^2}{4\pi r_2^2} = \frac{1}{4}, which implies \frac{r_1}{r_2} = \frac{1}{2}. The ratio of their volumes is \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = (\frac{r_1}{r_2})^3 = (\frac{1}{2})^3 = \frac{1}{8}.

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