Question-159135

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

Difficult to understand due to few steps.

$$\mathrm{Difficult}\:\mathrm{to}\:\mathrm{understand}\:\mathrm{due}\:\mathrm{to} \\ $$$$\mathrm{few}\:\mathrm{steps}. \\ $$

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=2 ⇒ r_2 =1 r_1 =r (2−r)^2 −r^2 =(1+r)^2 −(1−r)^2 ⇒ 4−4r=4r ⇒ r=1/2 %area=((1−((1/2)+(1/4)))/1)×100=25

$${let}\:{outer}\:{radius}=\mathrm{2}\:\Rightarrow\:{r}_{\mathrm{2}} =\mathrm{1} \\ $$$${r}_{\mathrm{1}} ={r} \\ $$$$\left(\mathrm{2}−{r}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} =\left(\mathrm{1}+{r}\right)^{\mathrm{2}} −\left(\mathrm{1}−{r}\right)^{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{4}−\mathrm{4}{r}=\mathrm{4}{r} \\ $$$$\Rightarrow\:\:\:{r}=\mathrm{1}/\mathrm{2} \\ $$$$\%{area}=\frac{\mathrm{1}−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{1}}×\mathrm{100}=\mathrm{25} \\ $$$$ \\ $$

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