Question

The diameter of the wheel of a bullock cart is 56 cm. Find the number of rotations to cover a distance of 2.2 km.

Answer 1

Hint: Circumference of the wheel is the total distance around the wheel. Thus, in one rotation the wheel moves a total of its circumference. By just knowing the radius (that is $\dfrac{{diameter}}{2}$ ), we can find the circumference using the formula ‘’.

Complete step-by-step answer:
Since, the diameter of the wheels of a bullock cart is given,
Therefore, radius of the wheel $ = \dfrac{{diameter}}{2}$
 $\begin{array}{l}
 = \dfrac{{56}}{2}\\
 = 28cm
 \end{array}$
Distance covered by wheels in one rotation = circumference of the wheel
And we know that,
Circumference of the wheel =
Where, ‘r’ is the radius of the wheel.
Therefore, distance covered in one rotation =
= $\begin{array}{l}
2 \times \dfrac{{22}}{7} \times 28\\
 = 176cm
\end{array}$
Means, in one rotation, the wheel covers a distance of 176cm.
Let us put this in a reverse way.
A distance of $176cm = 1 \cdot 76m$ is covered by the wheel in 1 rotation.
Therefore,
A distance of 1 m is covered by the wheel in $\dfrac{1}{{1 \cdot 76}}$ rotations.
Hence,
A distance of $2 \cdot 2km = 2200m$ is covered by the wheel in $\dfrac{1}{{1 \cdot 76}} \times 2200$ rotations = $1250$
Therefore,
The wheel rotates 1250 times to cover a distance of 2.2km.

Note: Here in the question it becomes very important for the students to convert units. The diameter of the wheel is given in centimeters while the total distance covered by the wheel is given in kilometers. So, it becomes important for the students to convert these different units into the same in order to get the answer.