Question

The wheel of a cycle covers 660 m by making 500 revolutions. What is the diameter of the wheel (in cm)

Answer 1

Hint: Divide the total distance covered by the number of revolutions to find the distance covered in one revolution. The distance covered in one revolution is the circumference of the wheel. Use the formula of circumference of the wheel, $C = 2\pi r$ to calculate the radius of the wheel. Then find the diameter of the wheel as diameter is double the radius. At last, convert the unit into cm.

Complete step-by-step answer:
We are given that the wheel covers a distance of 660 m.
Also, the number of revolutions used to cover the given distance is 500.
The distance covered can be calculated using the formula $\dfrac{{{\text{distance covered}}}}{{{\text{number of revolutions}}}}$.
Thus, distance covered in 1 revolution is, $\dfrac{{600}}{{500}} = 1.32m$
The distance covered by a wheel is equal to the circumference of the wheel.
Circumference of a circle is given by $2\pi r$ where $r$ is the radius.
Therefore, we have
$
  2\pi r = 1.32 \\
  r = \dfrac{{1.32}}{{2\pi }} \\
$
Use \[\pi = \dfrac{{22}}{7}\] in the above equation.
$r = \dfrac{{1.32 \times 7}}{{2\left( {22} \right)}} = 0.21m$
Diameter is double the radius, hence, we get, diameter =0.42m
But we need an answer in cm.
As, 1m=100cm, hence multiply 0.42 by 100 to convert the unit in cm.
Therefore, the diameter of the wheel is 42 cm.

Note: The distance covered in one revolution is the circumference of the wheel. Also, diameter is half the radius. After calculating the diameter using the circumference, change the unit from metre to centimetre.