Question

What is the radius of the circle if the angle of sector is 90° and the area of tge circle is 196 CM2

Answer 1

Step-by-step explanation:

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Answer 2

$\large{ \sf \underline{Given - }}$

$\sf \dashrightarrow \: Angle \: of \: sector = 90 \degree$

$\sf \dashrightarrow \: Area \: of \: the \: circle = 196 \: cm ^2$

$\large{ \sf \underline{To \: find - }}$

$\sf \dashrightarrow \: Radius \: of \: the \: circle = \: ?$

$\large{ \sf \underline{Solution - }}$

$\sf \dashrightarrow Area \: of \: sector = \dfrac{ \theta}{360 \degree} \times \pi r ^{2}$

$\sf Here \: \theta = 90 \degree$

$\bf Now,$

$\sf Substitute \: the \: values,$

$\sf \dashrightarrow 196 = \dfrac{ 90 \degree }{ \cancel{360 }\degree} \times \dfrac{ \cancel{22}}{7} \times r ^{2}$

$\sf \dashrightarrow 196 = \dfrac{ \cancel{90 }\degree }{ \cancel{180 }}\times \dfrac{ 11}{7} \times r ^{2}$

$\sf \dashrightarrow 196 = \dfrac{ 1 }{ 2}\times \dfrac{ 11}{7} \times r ^{2}$

$\sf \dashrightarrow 196 = \dfrac{ 11}{2 \times 7} \times r ^{2}$

$\sf \dashrightarrow 196 = \dfrac{ 11}{14} \times r ^{2}$

$\sf \dashrightarrow r ^{2} = \dfrac{14 \times 196}{11}$

$\sf \dashrightarrow r ^{2} = \dfrac{2744}{11}$

$\sf \dashrightarrow r = \pm \sqrt{\dfrac{2744}{11}}$

$\sf \dashrightarrow r = \pm \dfrac{14 \sqrt{154} }{11}$

$\sf \dashrightarrow r = \dfrac{14 \sqrt{154} }{11} \: \: \: or \: \: - \dfrac{14 \sqrt{154} }{11}$

$\bf Hence,$

$\sf \dashrightarrow \: Radius \: of \: the \: circle = \: \dfrac{14 \sqrt{154} }{11} \:cm \: \: \: or \: \: - \dfrac{14 \sqrt{154} }{11} \: cm$