Question

what is the area of a sector of angle P ( in degree) of a circle with radius R cm. ( class 10 )

plz solve it...​

Answer 1

Given : Angle of Sector is P⁰and Radius of circle is R .

Need To Find : Area of Sector .

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❍ Formula for Finding area of the Sector is given by :

$\frak {\underline {\dag As, \:We\:know\:that\;:}}$

$\qquad \qquad \underline {\boxed {\sf{ \bigstar Area\:of\:Sector \:_{(Circle)} = \dfrac{\theta}{360\degree} \times \pi r^{2}}}}$

Where ,

• $\theta$ is angle of Sector of the circle and r is the Radius of Circle .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \qquad :\implies \sf{ Area\:of\:Sector \:_{(Circle)} = \dfrac{p\degree}{360\degree} \times \pi R^{2}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {Area\:of\:Sector \:_{(Circle)} = \dfrac{p\degree}{360\degree} \times \pi R^{2}  }}}}\:\bf{\bigstar}$

Or ,

[ In M.C.Q we don't have any option like that .]

So In this case ,

• Multiply Both Numerator and Denominator by 2 .

$\qquad \qquad :\implies \sf{ Area\:of\:Sector \:_{(Circle)} = \dfrac{p\degree}{360\degree} \times \pi R^{2}\times \dfrac{2}{2}}$

$\qquad \qquad :\implies \sf{ Area\:of\:Sector \:_{(Circle)} = \dfrac{p\degree}{720\degree} \times 2\pi R^{2} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {Area\:of\:Sector \:_{(Circle)} = \dfrac{p\degree}{720\degree} \times 2\pi R^{2}  }}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Area\:of\:Sector \:_{(Circle)} =\bf{ \dfrac{p\degree}{720\degree} \times 2\pi R^{2}  }}}}$

Or,

⠀⠀⠀⠀⠀$\underline{ \mathrm { \bf{Area \:of\:sector\:_{(Circle)} = \dfrac{p\degree}{360\degree} \times \pi R^{2}  }}}$

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