Question

a race track is in the from of a ring whose inner circumference is 528m&the outer circumference is 616m.find the width of the track
$take\pi = 2upon7$
​

Answer 1

$\huge \underline{ \fbox{Answer}}$

$\large \underline{\underline{\underline{\frak{ \color{red}{Given:::}}}}}$

$\sf \mapsto{Inner \: circumference \: of \: circle=528m}$

$\sf \mapsto{ Outer \: circumference \: of \: circle=616m}$

$\large \underline{\underline{\underline{\frak{ \color{blue}{To \: find:::}}}}}$

$\sf \leadsto{Width \: of \: the \: track. }$

$\large \underline{\underline{\underline{\frak{ \color{indigo}{Formula \: used:::}}}}}$

$\maltese \boxed {\rm{{Circumference \: of \: circle = {2 {\pi}r}}}} \maltese$

$\maltese \boxed {\rm{Width \: of \: the \: track=radius_{(2)}-radius_{(1)}}} \maltese$

$\large \underline{\underline{\underline{\frak{ \color{i}{Concept \: used:::}}}}}$

$\sf{First,we \: find \: the \: outer \: radius(r_2) \: and }$

$\sf{inner \: radius (r_1) \: of \: the \: circle \: ,then, \: we }$

$\sf{also \: find \: the \: width \: of \: the \: track.}$

$\large \underline{\underline{\underline{\frak{ \color{peru}{According \: to \: Question:::}}}}}$

${ ::{\implies{\sf{{Outer \: circumference \: of \: circle = {2 {\pi}r_2}}}} }}$

${ ::{\implies{\sf{{616m = {2 \times { \frac{22}{7} \times }r_2}}}} }}$

${ ::{\implies{\sf{{r_2 = \frac{616 \times 7}{2 \times 22} }}} }}$

${ ::{\implies{\sf{{r_2 = { \xcancel {\frac{616 \times 7}{2 \times 22 }} }= 98m}}} }}$

${ ::{\implies{\sf{{Inner \: circumference \: of \: circle = {2 {\pi}r_1}}}} }}$

${ ::{\implies{\sf{{528m = {2 \times { \frac{22}{7} \times }r_1}}}} }}$

${ ::{\implies{\sf{{r_1 = \frac{528m\times 7}{2 \times 22} }}} }}$

${ ::{\implies{\sf{{r_1 = { \xcancel{\frac{528m\times 7}{2 \times 22}} = 96m }} }}}}$

${::{ \implies{\sf{Width \: of \: the \: track=radius \: of \: outer \: circle_{(2)}-radius \: of \: inner \: circle_{(1)}}}}}$

${::{ \implies{\sf{Width \: of \: the \: track=98m - 96m}}}}$

${::{ \implies{\sf{Width \: of \: the \: track=2m}}}}$

$\large \underline{ \pink{\frak{Hence, }}}$

${{ \rightarrow{\sf{Width \: of \: the \: track=2m}}}}$

$\large \underline{\underline{\underline{\frak{ \color{cyan}{Know \: more:::}}}}}$

${ \boxed{ \begin {array}{ |c|c| } \hline \sf Circumference \: of \: circle& \sf 2{\pi}r \\ \hline \sf Area \: of \: circle& {\pi} {r}^{2} \\ \hline \sf Radius \: of \: circle& \sf\frac{Diameter}{2} \\ \hline \sf Diameter \: of \: circle& \sf\frac{Radius}{2} \\ \end{array}}}$

_________________________________________________________