Question

a circular pond is surrounded by a 2 meter wide circular path. If outer circumference is 44cm what is the inner circumference

Answer 1

AnswEr :

$\bold{Given} \begin{cases}\sf{Outer \:Circumference=44m} \\ \sf{Width=2m}\\ \sf{Inner \:Circumference=?}\end{cases}$

$\begin{center}\setlength{\unitlength}{1.3 pt}\begin{picture}(100,100)(0,0)\put(0,0){\circle{50}} \put(0,0){\circle{22}} \put(0,0){\circle*{1.5}}\put(-16,0){\line(1,0){31.5}}\put(-15,1.5){ 2 }\end{picture}\setlength{\unitlength}{1 pt}\end{center}$

• Let's Head to the Question Now :

$\implies \tt Outer \: Circumference = 2\pi R$

$\implies \tt 44m = 2 \times \dfrac{22}{7} \times R$

$\implies \tt \cancel{44m} \times \dfrac{7}{ \cancel{22 \times 2}} = R$

$\implies \red{\tt R = 7m}$

$\rule{300}{1}$

⇒ Inner Radius ( r ) = Outer Radius - Width

⇒ Inner Radius ( r ) = 7m - 2m

⇒ Inner Radius ( r ) = 5 m

$\rule{300}{2}$

$\longrightarrow \tt Inner \: Circumference = 2\pi\:r$

$\longrightarrow \tt Inner \: Circumference = 2 \times \dfrac{22}{7} \times 5m$

$\longrightarrow \tt Inner \: Circumference = \dfrac{220}{7}m$

$\longrightarrow\boxed{\red{\tt Inner \: Circumference = 31.42m}}$

⠀

∴ Inner Circumference will be 31.42 m

Answer 2

$\Huge{\red{\sf{Hey!}}}$

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

--------------------------------

$\Large{\underline{\bf{Circumfrence \: of \: Outer \: Circle}}}$

We have formula for Circumference :

$\Large \displaystyle \implies {\underline{\boxed{\sf{2 \pi r}}}}$

Put Values

⇒ 44 = 2(22/7) * r

⇒44 = 44/7 * r

⇒r/7 = 1

⇒r = 7 m

$\large {\sf{{\blue{Outer \: Radius \: is}} \: {\red{7 \: m}}}}$

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Now,

$\Large{\underline{\bf{Radius \: of \: Inner \: Circle :}}}$

⇒Inner Radius = Outer Radius - Width

⇒Inner Radius = 7 - 2

⇒Inner Radius = 5 m

$\large {\sf{{\blue{Inner \: radius \: is}} \: {\red{5 \: m}}}}$

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Now,

$\Large {\underline{\bf{Inner \: Radius }}}$

Again use Formula for Circumference of circle

Put Values

⇒Inner Circumference = 2(22/7)*(5)

⇒Inner Circumference = (44/7)*5

⇒Inner Circumference = 220/7

⇒Inner Circumference = 31.42

$\large {\sf{{\blue{Inner \: Circumfrence \: is}} \: {\red{31.42 \: m}}}}$