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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Answer 1

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

• Perimeter = 25cm

• Radius = 8cm

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

• Area of sector

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

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

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

$\sf → 25 =8+8+area \:of \:ACB$

$\sf → Area \:of\: ACB=25-8+8$

$\sf → Area \:of \:ACB=9cm$

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

Area of sector = ½ × radius × arc

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

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

$\sf → Area\:of\:sector=36cm^2$

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

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

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