Question

A race track is in from of a ring whose inner circumference is 264m and the outer circumference is 308m find the width of the track

Answer 1

$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,

Circumference of inner ring of race track $C_{i} = 264\: m$

Circumference of outer ring of race track $C_{o} = 308\: m$

$\underline{\huge{\textsf{Step-1:}}}$
Find radius of Inner ring of race track and Outer ring of race track

Shape of Race track = Ring
$\implies \textsf{Concentric Circles}$

For a circle
We have,
$\bigstar \textsf{Circumference = 2 \pi \times Radius}$

$\implies C_{i} = 2 \pi r_{i}$

Substituting $C_{i}$

$\implies 264\: m = 2 \pi r_{i}$

$\implies r_{i} = \dfrac{264}{2\pi}\: m$



$\implies C_{o} = 2 \pi r_{o}$

Substituting $C_{o}$

$\implies 308\: m = 2 \pi r_{o}$

$\implies r_{o} = \dfrac{308}{2\pi}\: m$

$\underline{\huge{\textsf{Step-2:}}}$
Find the width of the Race track

$\textsf{Width of the Race track = Radius of Outer ring of Race track - Radius of Inner ring of Race track}$

$\implies \textsf{Width of the Race track W = r_{o} - r_{i} }$

Substituting Values

$\implies W = \dfrac{308}{2\pi}\: m - \dfrac{264}{2\pi}$

$\implies W = \dfrac{308 - 265}{2\pi}\: m$

$\implies W = \dfrac{44}{\frac{2(22)}{7}}\: m$

$\implies W = \dfrac{44}{\frac{44}{7}}\: m$

$\implies W = 7\: m$

$\therefore$
$\bigstar \textbf{Width\: of\: the\: race\: track = \underline{\underline{\large{7\: m}}}}$