# Question-142017

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
$${thank}\:{you}\:{mister}\:{W}. \\$$$$\\$$