Question

If the circumference of two circles are in the ratio 2 ratio 3 what is the ratio of their areas

Answer 1

$Let \: r \: and \: R \: are \: radii \: of \: circles$

$Ratio \: of \: circumstances = 2 : 3 \: (given)$

$\implies \frac{2\pi r }{2 \pi R } = \frac{2}{3}$

$\implies \frac{ r }{ R } = \frac{2}{3} \: ---(1)$

$\implies Ratio \: of \: areas = \frac{\pi r^{2}}{\pi R^{2}} \\= \big( \frac{r}{R}\big)^{2}\\=\big( \frac{2}{3}\big)^{2}\\=\frac{4}{9} \\= 4 : 9$

Therefore.,

$\red {Ratio \: of \: areas} \green { = 4:9}$

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Answer 2

Step-by-step explanation:

So, the ratio of the areas of two circles is 4:9