Question

Find the length of the arc and area of the sector of a circle of radius 7cm and sector angle 120°

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ length \ of \ the \ arc \ and \ area \ of \ the}$

$\sf{sector \ are \ 14.7 \ cm \ and \ 51.45 \ cm^{2}}$

$\sf{respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{Angle \ of \ sector(\theta)=120^\circ}}$

$\sf{\implies{Radius (r)=7 \ cm}}$

$\sf\pink{To \ find:}$

$\sf{Length \ of \ the \ arc \ and \ area \ of \ the \ sector.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\boxed{\sf{Length \ of \ arc(l)=\frac{\theta}{360}\times2\pi\times \ r}}$

$\sf{\therefore{Length \ of \ arc(l)=\frac{120}{360}\times2\times\frac{22}{7}\times7}}$

$\sf{\therefore{Length \ of \ arc(l)=\frac{44}{3}}}$

$\sf{\therefore{Length \ of \ arc(l)=14.7 \ cm \ (approx)}}$

$\boxed{\sf{Area \ of \ sector=\frac{Length \ of \ arc\times \ Radius}{2}}}$

$\sf{\therefore{Area \ of \ sector=\frac{14.7\times7}{2}}}$

$\sf{\therefore{Area \ of \ sector=14.7\times3.5}}$

$\sf{\therefore{Area \ of \ sector=51.45 \ cm^{2}}}$

$\sf\purple{\tt{\therefore{The \ length \ of \ the \ arc \ and \ area \ of \ the}}}$

$\sf\purple{\tt{sector \ are \ 14.7 \ cm \ and \ 51.45 \ cm^{2}}}$

$\sf\purple{\tt{respectively.}}$

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{Find \: the \: length \: of \: the \: arc \: and \: area}$

$\rm{of \: the \: sector \: of \: a \: circle \: of }$

$\rm{radius \: 7 \: cm \: and \: sector \: angle \: 120 °}$

_________________________________________

$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\rm\red{the \: length \: of \: the \: arc \: and \: area \: of \: the }$

$\rm\red{sector \: are \: 14.7 \: cm \: and \: 51.45 \: {cm}^{2} }$

$\rm\red{respectively}$

_________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{\implies{Angle \: of \: sector(\theta)=120^\circ}}$

$\rm{\implies{Radius (r)=7 \: cm}}$

_________________________________________

$\sf\large\underline\blue{To \ Find}$

$\rm{Length \: of \: the \: arc \: and \: area \: of \: the \: sector.}$

_________________________________________

$\purple{\underline{\underline{\blue{\boxed{\boxed{\red{\star{\sf Solution:}}}}}}}}$

$\rm{\pink{\boxed{Length \ of \ arc(l) \ = \ \frac{\theta}{360}\times2\pi\times \ r}}}$

$\rm{\longrightarrow{Length \ of \ arc(l) \ = \ \frac{120}{360}\times2\times\frac{22}{7}\times7}}$

$\rm{\longrightarrow{Length \ of \ arc(l) \ = \ \frac{44}{3}}}$

$\rm{\longrightarrow{Length \ of \ arc(l) \ = \ 14.7 \ cm \ (approx \ value)}}$

$\rm{\pink{\boxed{Area \ of \ sector \ = \ \frac{Length \ of \ arc\times \ Radius}{2}}}}$

$\rm{\longrightarrow{Area \ of \ sector=\frac{14.7\times7}{2}}}$

$\rm{\longrightarrow{Area \ of \ sector \ = \ 14.7\times3.5}}$

$\rm{\longrightarrow{Area \ of \ sector \ = \ 51.45 \ cm^{2}}}$

$\rm\red{the \: length \: of \: the \: arc \: and \: area \: of \: the }$

$\rm\red{sector \: are \: 14.7 \: cm \: and \: 51.45 \: {cm}^{2}}$

$\rm\red{respectively}$

_________________________________________

$\rm\orange{Hope \ it \ helps \ :))}$