Question

A race track is in the form of a ring whose inner and outer circumferences are 44cm and 66cm respectively. Find the width of the track.
(a) 3.50 cm
(b) 1 cm
(c) 3.20 cm
(d) 3 cm

Answer 1

Hint: To specify a figure most fundamental quantities are perimeter and area. Perimeter can be defined as the total length of the boundary of a geometrical figure. So, using this definition we can easily solve our problem.

Complete step-by-step answer:
According to this problem, we are given that the circumferences of inner and outer radii of a race track in the form of a ring are 44cm and 66cm respectively. Let the outer radius be R and the inner radius be r of the circular race track.
Circumference of outer circle$=2\pi R=66cm$
$R=\dfrac{66}{2\pi }$
Circumference of inner circle$=2\pi r=44cm$.
$r=\dfrac{44}{2\pi }$
Now, the width of the circular track can be expressed as the difference of outer radius and inner radius of the track.
Width of circular track = R – r.
$\begin{align}
  & =\dfrac{66}{2\pi }-\dfrac{44}{2\pi } \\
 & =\dfrac{66-44}{2\pi } \\
 & =\dfrac{22}{2\pi } \\
 & =\dfrac{11}{\pi }cm \\
\end{align}$
By putting the value of $\pi $, the width of the circular track $=\dfrac{11}{3.14}=3.50m$.
Hence, the width of the circular track is 3.50 m.
Therefore, option (a) is correct.

Note: The key concept involved in solving this problem is the knowledge of circumference of a circle. This is a direct question and can be solved by using the difference of outer radius and inner radius of track. This problem is helpful in solving complex problems.