Question : If the surface area of two spheres is in the ratio 81 : 25, then what is the ratio of their radius?
Option 1: 5 : 8
Option 2: 7 : 9
Option 3: 5 : 7
Option 4: 9 : 5
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Correct Answer: 9 : 5
Solution : Let the radii of two spheres be $r, R$, respectively. According to the question, $\frac{4\pi r^2}{3\pi R^2}=\frac{81}{25}$ $⇒\frac{r^2}{R^2}=\frac{81}{25}$ $\therefore \frac{r}{R}=\frac{9}{5}$ Hence, the correct answer is 9 : 5.
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