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Question Number 98560 by I want to learn more last updated on 14/Jun/20

Commented by I want to learn more last updated on 14/Jun/20

$$\mathrm{Find}\mathrm{the}\mathrm{shaded}\mathrm{area}.$$

Answered by HamraboyevFarruxjon last updated on 14/Jun/20

$$\mathit{S}\left(\mathit{r}\mathit{o}\mathit{m}\mathit{b}\right)={\mathit{a}}^2\times \mathit{s}\mathit{i}\mathit{n}\mathit{\alpha }=81\times \mathit{s}\mathit{i}\mathit{n}70°$$$$\mathit{S}\left(\mathit{s}\mathit{e}\mathit{c}\mathit{t}\mathit{o}\mathit{r}\right)=\frac{70°}{360°}\times \mathit{\pi }\times 9^2=\frac{63\mathit{\pi }}{4}$$$$\mathit{S}\left(\mathit{s}\mathit{h}\mathit{a}\mathit{d}\mathit{e}\mathit{d}\right)=\mathit{S}\left(\mathit{r}\mathit{o}\mathit{m}\mathit{b}\right)-\mathit{S}\left(\mathit{s}\mathit{e}\mathit{c}\mathit{t}\mathit{o}\mathit{r}\right)=$$$$=81\mathit{s}\mathit{i}\mathit{n}70°-\frac{63\mathit{\pi }}{4}\approx 26,63$$

Answered by mr W last updated on 14/Jun/20

$$r=9cm$$$$\theta =70°=\frac{7\pi }{18}$$$$A_{shaded}=r^2(\sin \theta -\frac{\theta }{2})=9^2(\sin \frac{7\pi }{18}-\frac{7\pi }{36})$$$$=26.636{cm}^2$$

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