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Question Number 93125 by john santu last updated on 11/May/20

Commented by john santu last updated on 11/May/20

$$\mathrm{find}\mathrm{the}\mathrm{shaded}\mathrm{area}$$

Commented by i jagooll last updated on 11/May/20

$$\frac{\mathrm{r}}{6}=\frac{\mathrm{x}}{\mathrm{x}+2\mathrm{r}}\Rightarrow \mathrm{rx}+{2\mathrm{r}}^2=6\mathrm{x}$$$${2\mathrm{r}}^2=\mathrm{x}(6-\mathrm{r})\Rightarrow \mathrm{x}=\frac{{2\mathrm{r}}^2}{6-\mathrm{r}}...\left(\mathrm{i}\right)$$$$6^2=\mathrm{r}(2\mathrm{r}+\mathrm{x})\Rightarrow 36=\mathrm{r}(2\mathrm{r}+\frac{{2\mathrm{r}}^2}{6-\mathrm{r}})..\left(\mathrm{ii}\right)$$$$18=\mathrm{r}(\mathrm{r}+\frac{{\mathrm{r}}^2}{6-\mathrm{r}})\Rightarrow 18=\mathrm{r}\left(\frac{6\mathrm{r}}{6-\mathrm{r}}\right)$$$$18-3\mathrm{r}={\mathrm{r}}^2\Rightarrow {\mathrm{r}}^2+3\mathrm{r}-18=0$$$$(\mathrm{r}+6)(\mathrm{r}-3)=0\Rightarrow \mathrm{r}=3$$$$\mathrm{shaded}\mathrm{area}=\pi {\mathrm{r}}^2=9\pi$$

Commented by john santu last updated on 11/May/20

cool man ��������

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