Question

if tye ratio of the m circumference of two circles is 2:3,what is the ratio of their redii?​

Answer 1

Step-by-step explanation:

RatioofcirclesArea=94

Step-by-step explanation:

Let \: r,\: R \: are \: radii \: of \: two \: circlesLetr,Rareradiioftwocircles

\begin{gathered}Ratio \: of \: circumference \:\\ of \: two \: circles=2:3 \: (given)\end{gathered}Ratioofcircumferenceoftwocircles=2:3(given)

\implies \frac{2\pi r}{2\pi R}= \frac{2}{3}⟹2πR2πr=32

\implies \frac{r}{R}=\frac{2}{3}--(1)⟹Rr=32−−(1)

\begin{gathered}Now,\\Ratio \: of \: \\circles \: Area = \frac{\pi r^{2}}{\pi R^{2}}\end{gathered}Now,RatioofcirclesArea=πR2πr2

\begin{gathered}=\big(\frac{r^{2}}{R^{2}}\big)\\=\big(\frac{r}{R}\big)^{2}\\=\big(\frac{2}{3}\big)^{2}\\=\frac{4}{9}\end{gathered}=(R2r2)=(Rr)2=(32)2=94

Therefore,.

Ratio \: of \: circles \: Area =\frac{4}{9}RatioofcirclesArea=94

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