Question Number 63750 by Tawa1 last updated on 08/Jul/19
Commented by Prithwish sen last updated on 08/Jul/19
$$\mathrm{perimeter}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{A}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\pi\mathrm{r}\:\mathrm{unit} \\ $$$$\mathrm{perimeter}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{B}\:=\:\mathrm{2}\pi\mathrm{r}\:\mathrm{unit} \\ $$$$\mathrm{Circle}\:\mathrm{A} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{covers}\:\frac{\mathrm{2}}{\mathrm{3}}\pi\mathrm{r}\:\mathrm{in}\:\mathrm{1}\:\mathrm{time} \\ $$$$\therefore\:\mathrm{it}\:\mathrm{covers}\:\mathrm{2}\pi\mathrm{r}\:\mathrm{in}\:\frac{\mathrm{2}\pi\mathrm{r}}{\frac{\mathrm{2}}{\mathrm{3}}\pi\mathrm{r}}\:\:\mathrm{times}\:=\:\mathrm{3}\:\mathrm{times} \\ $$
Commented by Tawa1 last updated on 08/Jul/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Answered by MJS last updated on 08/Jul/19
$$\mathrm{perimeter}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{A}\:={p}_{{A}} \\ $$$$\mathrm{perimeter}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{B}={p}_{{B}} \\ $$$$\frac{{r}_{{B}} }{{r}_{{A}} }=\frac{{p}_{{B}} }{{p}_{{A}} }=\frac{\mathrm{3}}{\mathrm{1}}=\mathrm{3} \\ $$$$\Rightarrow\:\mathrm{answer}\:\left(\mathrm{b}\right) \\ $$
Commented by Tawa1 last updated on 08/Jul/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir},\:\mathrm{but}\:\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{how}\:\mathrm{it}\:\mathrm{is}\:\:\frac{\mathrm{3}}{\mathrm{1}} \\ $$
Commented by MJS last updated on 08/Jul/19
$${r}_{{A}} =\frac{{r}_{{B}} }{\mathrm{3}}\:\Leftrightarrow\:{r}_{{B}} =\mathrm{3}{r}_{{A}} \:\Leftrightarrow\:\frac{{r}_{{B}} }{{r}_{{A}} }=\mathrm{3} \\ $$$${p}_{{A}} =\mathrm{2}\pi{r}_{{A}} =\frac{\mathrm{2}\pi}{\mathrm{3}}{r}_{{B}} =\frac{\mathrm{1}}{\mathrm{3}}{p}_{{B}} \:\Leftrightarrow\:\frac{{p}_{{B}} }{{p}_{{A}} }=\mathrm{3} \\ $$
Commented by Tawa1 last updated on 08/Jul/19
$$\mathrm{I}\:\mathrm{appreciate}\:\mathrm{sir} \\ $$