Question

A bicycle wheel makes 5000 revolutions in making 11 km. Find the circumference and diameter of the wheel.

Answer 1

Hint: We will divide 11 by 5000 to find the distance covered in one revolution and it will equal to the circumference of the circle. We will then substitute the value of the circumference and $\pi = \dfrac{{22}}{7}$ in the formula, $2\pi r$ to determine the radius. Next, we will multiply the radius by 2 to find the diameter of the wheel.

Complete step-by-step answer:
We are given that a wheel make 5000 revolutions to cover 11 km.
We will find the distance covered in one revolution to find the circumference of the wheel.
To find the distance covered in one revolution, we will divide 11 by 5000.
$\dfrac{{11}}{{5000}}$
Therefore, the circumference of the wheel is $\dfrac{{11}}{{5000}}$ km.
It is known that circumference of the circle is $2\pi r$, where $r$ is the radius of the wheel.
$\dfrac{{11}}{{5000}} = 2\pi r$
We will substitute the value of $\pi = \dfrac{{22}}{7}$ to find the value of $r$.
$
  \dfrac{{11}}{{5000}} = 2\left( {\dfrac{{22}}{7}} \right)r \\
   \Rightarrow r = \dfrac{{11\left( 7 \right)}}{{5000\left( {44} \right)}} \\
   \Rightarrow r = 0.00035km \\
$
We will multiply the radius by 1000 to find the radius in m.
$r = 35m$
We know that diameter is twice the radius of the wheel.
Therefore, $2\left( {35} \right) = 70m$.

Note: The circumference of the wheel is the distance covered by the wheel in one revolution. Also, one must know that diameter is double the radius of the circle. And we can convert km into metres by multiplying it by 1000.