Question

the circumference of two circles are in ratio 5:6 . find the ratio of their area​

Answer 1

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

$\pink {Ratio \: of \: circumstances = 5:6 }\:(given)$

$\implies \frac{2\pi r }{ 2 \pi R} = \frac{5}{6}$

$\implies \frac{r}{R} = \frac{5}{6} \: ---(1)$

$Now, \:Ratio \: of \: Area's = \frac{ \pi r^{2}}{\pi R^{2}}\\= \big( \frac{r}{R}\big)^{2}\\= \big( \frac{5}{6}\big)^{2}\: [ From \:(1) ]$

$= \frac{25}{36} \\= 25 : 36$

Therefore.,

$\red {Ratio \: of \: Area's} \green = { 25 : 36}$

•••♪