Question Number 142017 by cherokeesay last updated on 25/May/21
Commented by cherokeesay last updated on 25/May/21
$$ \\ $$1) Calculate R 2) Calculate the% of the area of the hatched part compared to the area of the half disk of Radius R.
Commented by mr W last updated on 26/May/21
$${better}\:{solve}\:{this}: \\ $$
Commented by mr W last updated on 26/May/21
Answered by help last updated on 26/May/21
$$\mathrm{2}+\sqrt{\mathrm{3}} \\ $$
Answered by help last updated on 26/May/21
Commented by cherokeesay last updated on 26/May/21
$${thank}\:{you}\:{sir}\:! \\ $$$${very}\:{nice}. \\ $$
Answered by mr W last updated on 26/May/21
$$\left(\frac{\mathrm{3}}{{r}}−\frac{\mathrm{1}}{{R}}\right)^{\mathrm{2}} =\mathrm{2}\left(\frac{\mathrm{3}}{{r}^{\mathrm{2}} }+\frac{\mathrm{1}}{{R}^{\mathrm{2}} }\right) \\ $$$$\frac{\mathrm{3}{R}^{\mathrm{2}} }{{r}^{\mathrm{2}} }−\frac{\mathrm{6}{R}}{{r}}−\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\frac{{R}}{{r}}=\frac{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$$\Rightarrow{R}=\left(\mathrm{1}+\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}\right)\sqrt{\mathrm{3}}=\mathrm{2}+\sqrt{\mathrm{3}} \\ $$
Commented by cherokeesay last updated on 26/May/21
$${thank}\:{you}\:{mister}\:{W}. \\ $$$$ \\ $$