Question

50. The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes
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Answer 1

Step-by-step explanation:

$\frac{4\pi {r}^{2} }{4\pi {d}^{2} } = \frac{1}{4} \\ \frac{ {r}^{2} }{ {d}^{2} } = \frac{1}{4} \\ \frac{r}{d} = \sqrt{ \frac{1}{4} } \\ \frac{r}{d} = \frac{1}{2} \\ let \: r = 1x \: and \: d = 2x \\ volume \: (1) \: = \frac{4}{3} \pi {x}^{3} \\ volume \: (2) = \frac{4}{3}\pi(2x) {}^{3} = \frac{32\pi {x}^{3} }{3} \\ \frac{v1}{v2} = \frac{ \frac{4}{3}\pi {x}^{3} }{ \frac{32}{3} \pi {x}^{3} } = \frac{1}{8}$