Question Number 160654 by Avijit007 last updated on 04/Dec/21
Answered by som(math1967) last updated on 04/Dec/21
$${let}\:{radius}\:{of}\:{semicircle}\:{rcm} \\ $$$$\therefore\:\boldsymbol{{r}}^{\mathrm{2}} =\left(\boldsymbol{{r}}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{2}\boldsymbol{{r}}−\mathrm{1}=\mathrm{9} \\ $$$$\therefore\boldsymbol{{r}}=\mathrm{5}\boldsymbol{{cm}} \\ $$$$\boldsymbol{{O}}{R}=\mathrm{5}−\mathrm{1}=\mathrm{4}{cm} \\ $$$$\boldsymbol{{A}}{r}\boldsymbol{{ea}}\:\boldsymbol{{of}}\:\boldsymbol{{shaded}}\:\boldsymbol{{region}} \\ $$$$\:=\frac{\mathrm{1}}{\mathrm{4}}×\boldsymbol{\pi}×\mathrm{5}^{\mathrm{2}} −\mathrm{4}×\mathrm{3} \\ $$$$=\left(\mathrm{6}.\mathrm{25}\boldsymbol{\pi}−\mathrm{12}\right)\boldsymbol{{cm}}^{\mathrm{2}} \\ $$$$\boldsymbol{{B}}\:\boldsymbol{{ans}} \\ $$
Commented by Tawa11 last updated on 05/Dec/21
$$\mathrm{Great}\:\mathrm{sir} \\ $$