Question

The measure of a central angle of a circle angle of a circle is 150degree and radius of a circle is 21 cm .find the area of the sector

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{ solution}}}}$

$\star \underline{For\: a \:circle \:of\: radius\:\red{ <strong>R</strong><strong>}</strong>} \\ \underline{and\: of \:central \:angle \: \red{\theta}}\\</p><p>\bf\implies\boxed{\red{Area}_\blue{sector}=\frac{\pi R{}^{2}}{360\degree}\times \theta}$

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given

$\rightarrow\bf R=21 \:cm\\ \rightarrow \bf\theta=150\degree$

$\bf\therefore\bf \red{Area}_{sector}=\frac{\frac{22}{7}\times 21{}^{2}}{360\degree}\times 150\degree$

$\bf \red{Area}_{sector}=\frac{\frac{22}{\cancel7}\times \cancel{21}\times21}{36\cancel0\degree}\times 15\cancel0\degree\\ \bf \red{Area}_{sector}=\frac{\cancel{22}\times\cancel3\times\cancel{21}\times15}{\cancel{36}}\\ \bf \red{Area}_{sector}=\frac{11\times7\times15}{2}\\ \bf \red{Area}_{sector}=\frac{1155}{2}\\ \boxed{ \bf \red{Area}_{sector}=577.5\:cm{}^{2}}$

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