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Question-185685




Question Number 185685 by cherokeesay last updated on 25/Jan/23
Answered by mr W last updated on 25/Jan/23
(r/(2R−r))=sin 30°=(1/2)  ⇒(R/r)=(3/2)  ((green)/(yellow))=((πr^2 )/(πR^2 −πr^2 ))=(1/(((3/2))^2 −1))=(4/5)=80%
$$\frac{{r}}{\mathrm{2}{R}−{r}}=\mathrm{sin}\:\mathrm{30}°=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{{R}}{{r}}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\frac{{green}}{{yellow}}=\frac{\pi{r}^{\mathrm{2}} }{\pi{R}^{\mathrm{2}} −\pi{r}^{\mathrm{2}} }=\frac{\mathrm{1}}{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} −\mathrm{1}}=\frac{\mathrm{4}}{\mathrm{5}}=\mathrm{80\%} \\ $$
Commented by cherokeesay last updated on 25/Jan/23
thank you sir.
$${thank}\:{you}\:{sir}. \\ $$

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