Question

The wheel of a bullock cart has a diameter of 1.4m. How many rotations will the wheel complete as the cart travels 1.1km?

Answer 1

Hint: Find the distance travelled by wheel in one rotation by the formula of circumference of the circle and then apply the unitary method to find the no of rotations while travelling 1.1kms.

Complete Step-by-step answer:
Given, diameter of wheel = 1.4m,
$\therefore $radius of wheel = 0.7m.

Now, we know, the circumference of a circle is the length of the thread required to complete the circle. So, we can say that the distance travelled by the wheel in one rotation is equal to the circumference of the circle.
We know, the circumference of the circle with radius r is given as $Circumference=2\pi r$ .
So, distance travelled the wheel in one rotation \[=2\pi r\]
\[\begin{align}
  & =2\times \dfrac{22}{7}\times 0.7 \\
 & =4.4m. \\
\end{align}\]
We now use the unitary method to find the number of rotations to travel a distance of 1.1 km.
In one rotation, the wheel covers 4.4 m.
Let us assume that in \[x\] rotations, the wheel covers 1.1 km = 1100m.
1 x 4.4 = 4.4
\[x\] x 4.4 = 1.1 x 1000
\[\Rightarrow x=250\]
Hence, the answer is 250 rotations.

Note: While comparing entities, make sure they are in the same units. In the above problem, the circumference of the wheel is in metres and the distance covered is in kilometres. So, we have converted the distance covered into metres.