Question

If the ratio of the areas of two circles is 4:1, what is the ratio of their circumferences?

Answer 1

$hey \: mate \: your \: answer \: here$

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$area \: of \: a \: circle \: = \pi {r}^{2} \\ \\ ratio \: of \: areas \: of \: two \: circles \: are \: \\ = > \frac{\pi \: {r1}^{2} }{\pi \: {r2}^{2} } = \frac{ {r1}^{2} }{ {r2}^{2} } = \frac{4}{1} \\ = > {r1}^{2} = 4 {r2}^{2} \\ taking \: square \: root \: of \: both \: the \: sides \\ = > \sqrt{ {r1}^{2} } = \sqrt{4 {r2}^{2} } \\ = > r1 = 2r2 \\ their \: circumferences \\ = 2\pi \: r1 \: and \: 2\pi \: r2 \\ ratio= \frac{2\pi \: r1}{2\pi \: r2} = \frac{r1}{r2} \\ = \frac{2r2}{r2} = \frac{2}{1}$

Hence the answer is 2:1

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