Question

A race track is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width of the track.

Answer 1

Hint: The concept here to be used is to find radius of both inner track and outer track and when we get \[{{r}_{1}}\]and\[{{r}_{2}}\] then from the diagram we can see that width is equal to difference in the radius of both tracks \[\left( {{r}_{1}}-{{r}_{2}} \right)\] when \[{{r}_{1}}>{{r}_{2}}\]

Complete step by step solution:

Also formula for circumference\[=2\pi r\]
\[\Rightarrow \]Inner circumference of track \[=352\]m
Let us assume radius to be \[{{r}_{2}}\]
\[2\pi {{r}_{2}}=352m\] ……. 1
\[\Rightarrow \]Outer circumference of race track \[=396m\]
Let us assume radius to be \[{{r}_{1}}\]
\[2\pi {{r}_{1}}=396m\]
Solving 1 and 2
\[{{r}_{2}}=\dfrac{352}{2\pi }\] \[{{r}_{1}}=\dfrac{396}{2\pi }\]
Now width of track is
$\Rightarrow {{r}_{1}}-{{r}_{2}}$ $\left\{ \because {{r}_{1}}>{{r}_{2}} \right\}$
 $\Rightarrow \dfrac{396}{2\pi }-\dfrac{352}{2\pi }$
$\Rightarrow \dfrac{396-352}{2\pi }$
$\Rightarrow \dfrac{44}{2\pi }$
$\Rightarrow 7.00282$
So the width of the track is 7.00282 m.

Note: You can also find the width from finding the diameters of respective tracks rather than finding radius of the tracks
Then the formula of width \[\Rightarrow \dfrac{{{d}_{1}}-{{d}_{2}}}{2}\]
 Where \[{{d}_{1}}\]and \[{{d}_{2}}\]are respective track diameters.