Question

How many times a wheel of radius $28cm$ must rotate to go $352m$? (Take $\pi =\dfrac{22}{7}$ )

Answer 1

Hint: We need to find the number of revolutions a wheel would require to cover a distance of 352m. In one revolution the wheel covers a distance equal to its circumference which is given by the formula $'2\pi r'$ where ‘r’ is the radius of the wheel. Therefore, the total number of revolutions required will be equal to the total distance needed to be covered by the wheel divided by the wheel’s circumference.

Complete step-by-step solution:

First, we will calculate the circumference of the wheel.
Here, it is given that the radius of the circle $=28cm$
Therefore, the circumference of the wheel is given as follows:
$\begin{align}
  & \Rightarrow 2\pi r \\
 & r=28cm \\
\end{align}$
$\begin{align}
  & \Rightarrow 2\pi \left( 28 \right) \\
 & \Rightarrow 2\times \dfrac{22}{7}\times 28 \\
 & \Rightarrow 2\times 22\times 4 \\
 & \Rightarrow 176cm \\
\end{align}$
Therefore, the distance covered by the wheel in revolution is equal to 176cm
Now, it is given that the wheel needs to cover the distance of 352m.
Here the circumference is in ‘centimeters’ and the distance required to be covered is in ‘meters’. Therefore, we’ll need to change ‘meters’ into ‘centimeters’.
352m would be converted into centimetres as follows:
$\begin{align}
  & \Rightarrow 1m=100cm \\
 & \Rightarrow 352m=35200cm \\
\end{align}$
Now, to calculate the total number of revolutions we will need to divide the total distance needed to be covered by the circumference of the wheel.
Therefore,
$\begin{align}
  & revolutions=\dfrac{35200}{176} \\
 & revolutions=200 \\
\end{align}$
Thus, total number of revolutions required by the wheel to cover a distance of $352m=200$

Note: Don’t forget to convert the unit so that the units will be the same otherwise it will result in a wrong answer. Here we have converted ‘meters’ into ‘centimeters’ but any of the two units can be converted into the other, the answer will come out to be the same in both cases.