Question Number 159135 by cherokeesay last updated on 13/Nov/21
Commented by Rasheed.Sindhi last updated on 13/Nov/21
$${I}'{ve}\:{now}\:{understood}\:{completely}\: \\ $$$${although}\:\:{difficultly}. \\ $$$${I}\:{want}\:{to}\:{say}\:{only}\:{that}\:{the}\:{answer} \\ $$$${should}\:{be}\:{somewhat}\:{more}\:{detailed} \\ $$$${in}\:{order}\:{that}\:{the}\:{persons}\:{who}\:{are} \\ $$$${not}\:{sharp}\:{enough}\:{like}\:{me}\:{also}\:{can}\:{under}- \\ $$$${stand}\:{easily}.\:\mathcal{T}{he}\:{diagram}\:{is}\:{ok}. \\ $$
Commented by Rasheed.Sindhi last updated on 13/Nov/21
$$\vee\:\cap\mathrm{i}\subset\in! \\ $$
Commented by Rasheed.Sindhi last updated on 13/Nov/21
$$\mathrm{Difficult}\:\mathrm{to}\:\mathrm{understand}\:\mathrm{due}\:\mathrm{to} \\ $$$$\mathrm{few}\:\mathrm{steps}. \\ $$
Commented by cherokeesay last updated on 13/Nov/21
$${just}\:{follow}\:{these}\:{steps}\:{by}\:{taking}\:{a}\:{look} \\ $$$${at}\:{the}\:{diagram}. \\ $$
Answered by ajfour last updated on 13/Nov/21
$${let}\:{outer}\:{radius}=\mathrm{2}\:\Rightarrow\:{r}_{\mathrm{2}} =\mathrm{1} \\ $$$${r}_{\mathrm{1}} ={r} \\ $$$$\left(\mathrm{2}−{r}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} =\left(\mathrm{1}+{r}\right)^{\mathrm{2}} −\left(\mathrm{1}−{r}\right)^{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{4}−\mathrm{4}{r}=\mathrm{4}{r} \\ $$$$\Rightarrow\:\:\:{r}=\mathrm{1}/\mathrm{2} \\ $$$$\%{area}=\frac{\mathrm{1}−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{1}}×\mathrm{100}=\mathrm{25} \\ $$$$ \\ $$