10th Class Mathematics Areas Related to Circles Question Bank MCQs - Areas Related to Circles

A race track is in the form of a circular ring whose outer and inner circumferences are \[\text{396 m}\] and \[\text{352}\,\text{m}\] respectively. The width of the track is:

A) \[63\,\text{m}\]

B) \[56\,\text{m}\]

C) \[7\,\text{m}\]

D) \[3.5\,\text{m}\]

Correct Answer: C

Solution :

[c] Let R and r be the outer and inner radii of the track respectively,

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\pi R=396\] ...(1)

and \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\pi r=352\] ...(2)

Subtracting eqs.(2) from (1), we get

\[2\pi R-2\pi r=396-352\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\pi (R-r)=44\]

\[\therefore \] Width of the track

\[=R-r=\frac{44}{2\pi }=\frac{44}{\left( 2\times \frac{22}{7} \right)}=7\,m\]