Question

Area of a sector of a circle of radius 14cm is 154 cm2 . Find the length of the corresponding arc of the sector (22cm)

Answer 1

AnswEr:

$\bold{\underline{\sf{\blue{\:\: Given\:\:}}}}$

• Area of Sector = 154 cm
• Radius = 14 cm

To Find :-

Length of the Arc

Explanation:-

We know that,

$\longrightarrow\large\boxed{\sf{\red{Area \:of\: Sector\:=\: \dfrac{\theta}{360} \times\pi r^2}}}$

$\longrightarrow\sf\: 154 = \dfrac{\theta}{360} \times \dfrac{22}{7} \times\:14^2$

$\longrightarrow\sf\: 154 = \dfrac{\theta}{360} \times\:616$

$\longrightarrow\sf\: \dfrac{154}{616} \:=\:\dfrac{\theta}{360}$

$\longrightarrow\sf\: \dfrac{1}{4}\:=\:\dfrac{\theta}{360}$

$\longrightarrow\sf\: \theta\:=\: \dfrac{360}{4}$

$\longrightarrow\large{\underline{\boxed{\sf{\pink{\theta\:=\:90}}}}}$

$\rule{150}2$

Now, finding the length of the Arc

$\longrightarrow\large\boxed{\sf{\red{Length\:of\:Arc\:=\: \dfrac{\theta}{360}\times 2 \pi r}}}$

$\longrightarrow\sf\: \dfrac{90}{360} \times 2\times \dfrac{22}{7} \times 14$

$\longrightarrow\sf\: \dfrac{1}{4} \times 88$

$\longrightarrow\sf\: \dfrac{88}{2}$

$\longrightarrow\large\boxed{\sf{\pink{22\:cm}}}$

$\dag\:\:\bold{\underline{\sf{Hence,\: Length\:of\:the\:Arc\;is\:22\:cm.}}}$

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

We know that,

$\Large {\implies{\boxed{\boxed{\sf{Area \: of \: sector = \frac{\theta}{360} \times \pi r^2}}}}}$

$\tt{→\: 154 = \dfrac{\theta}{360} \times \dfrac{22}{7} \times\:14^2}$

$\tt{→\: 154 = \dfrac{\theta}{360} \times\:616}$

$\tt{→\: \dfrac{154}{616} \:=\:\dfrac{\theta}{360}}$

$\tt{→\: \dfrac{1}{4}\:=\:\dfrac{\theta}{360}}$

$\tt{→\: \theta\:=\: \dfrac{360}{4}}$

$\Large{\boxed{\boxed{\sf{\theta\:=\:90}}}}[\tex]</p><p></p><p>[tex]\Large{\implies{\boxed{\boxed{\rm{Length \: of \:Arc = \dfrac{\theta}{360}\times 2 \pi r}}}}}$

$\tt{→ \dfrac{90}{360} \times 2\times \dfrac{22}{7} \times 14}$

$\tt{ →\dfrac{1}{4} \times 88}$

$\tt{→\dfrac{88}{2}}$

$\large\boxed{\sf{22\:cm}}$