Question

A wheel has a diameter of 84 cm. Find how many complete revolutions it must take to cover 792 metres.

Answer 1

Hint: We will find the circumference of the circle using the formula $2\pi r$. Here we have to convert the diameter into radius by dividing it by 2 as diameter = 2 $\times $ radius.

Complete step-by-step answer:

It is given in the question that a wheel has a diameter of 84 cm. And that the wheel has to cover 792 metres. We have to find the number of complete revolutions that the wheel must take to cover a distance of 792 metres.

We will first find the distance covered by the wheel in one complete revolution by finding the circumference of its circle. We know that the circumference of the circle is given by \[2\pi r\].
We have the diameter of the wheel as 84 cm, so we can write,
 $\begin{align}
  & \text{Radius of wheel}=\dfrac{\text{diameter}}{2} \\
 & =\dfrac{84}{2} \\
 & =42cm. \\
\end{align}$

The circumference of the circle is $2\pi r$. Substituting radius in it, we get
$\begin{align}
  & =2\times \dfrac{22}{7}\times 42 \\
 & =2\times 22\times 6 \\
 & =44\times 6 \\
 & =264cm \\
\end{align}$

We can convert 264 cm into metres by dividing it by 100 = 2.64, so we get the distance covered by the wheel in one complete revolution = 2.64 m.

Now, we will divide the total distance to be covered by the wheel by the distance covered in one revolution to get the total number of revolutions required by the wheel to complete the journey.

The total distance to be covered = 792 m
Distance covered in one complete revolution = 2.64 m.
So, the number of revolutions is,
$\begin{align}
  & =\dfrac{792}{2.64} \\
 & =300 \\
\end{align}$

Therefore, the wheel has to take 300 revolutions to cover the distance of 792 metres.

Note: You can solve this by keeping the circumference of the circle in cm itself. In that case you have to convert 792 metres into centimetres, which is 792 $\times $ 100 = 79200 cm. So, the total revolutions to be covered would be given as,
$\begin{align}
  & =\dfrac{79200}{264} \\
 & =300\text{ revolutions}. \\
\end{align}$