1. The perimeter of a circle of radius 8 cm is 25cm. what is the area of sector? a) 50cm b) 42cm c) 36cm d) 52cm? ​

Question

1. The perimeter of a circle of radius 8 cm is 25cm. what is the area of sector?
a) 50cm b) 42cm c) 36cm d) 52cm?

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Ella 3 weeks 2021-09-22T22:28:56+00:00 1 Answer 0 views 0

Answers ( )

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    2021-09-22T22:30:00+00:00

    \;\;\underline{\textbf{\textsf{ Given  :-}}}

    • Perimeter = 25cm

    • Radius = 8cm

    \;\;\underline{\textbf{\textsf{ To Find :-}}}

    • Area of sector

    \;\;\underline{\textbf{\textsf{ Solution  :-}}}

    \underline{\:\textsf{Firstly,  we need to find the area of triangle ABC  :}}

    \sf → Perimeter = OA+OB+ Area \:of\: ACB

    \sf → 25 =8+8+area \:of \:ACB

    \sf → Area \:of\: ACB=25-8+8

    \sf → Area \:of \:ACB=9cm

    ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

    \underline{\:\textsf{Now,  find the area of the sector }}

    Area of sector = ½ × radius × arc

    \sf → Area \:of\:sector = \dfrac{1}{2}×8×9

    \sf → Area\:of\: sector=\dfrac{1}{\cancel{2}}×{\cancel{8}}×9

    \sf → Area\:of\:sector=36cm^2

    \;\;\underline{\textbf{\textsf{ Hence-}}}

    \underline{\textsf{ The required area of sector is\textbf{ 36cm²}}}.

    ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

    \boldsymbol{\: Option\:C)\: is \: correct√}

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