Question

A bus has wheels of diameter \[1.4m\]. Travelling from one town to another, the wheels complete \[20,000\] rotations. Find the distance covered by the bus.
(A) \[88km\]
(B) \[44km\]
(C) \[8800m\]
(D) \[4400m\]

Answer 1

Hint: We are given that a bus has a wheel with a given diameter and it makes \[20,000\] rotations to travel from one town to the other and we are asked to calculate the distance covered by the train. We know that the wheel is in the shape of 2D circle. And the distance that will be covered in one rotation is equal to the circumference of the circle, which is, \[2\pi r\]. So, for \[20,000\] rotations, we will multiply the circumference by \[20,000\]. On solving, we will have the distance covered by the bus while travelling from one town to another.

Complete step-by-step solution:
According to the given question, we are given a bus which has wheels of diameter \[1.4m\]. The wheels complete \[20,000\] rotations while the bus travels from one town to other and we are asked to find the distance covered by the bus for the same.
The given diameter of the wheel is, \[d=1.4m\]
The radius of the wheel is, \[r=\dfrac{1.4}{2}=0.7m\]
We know that the wheel is in the shape of 2D circle. And the distance that will covered in one rotation is equal to the circumference of the circle, which is, \[2\pi r\].
So, the distance covered in \[20,000\] rotation of the wheel is,
\[= 20000\times 2\pi r\]
We will now substitute the known values and we get,
\[= 20000\times 2\times \dfrac{22}{7}\times 0.7\]
\[= 20000\times 2\times \dfrac{22}{7}\times \dfrac{7}{10}\]
Cancelling out the common terms, we get the expression as,
\[= 20000\times 2\times \dfrac{22}{10}\]
\[= 2000\times 2\times 22\]
\[= 88000m\]
\[= 88km\]
Therefore, the distance covered by the bus is (A) \[88km\].

Note: The formula for the circumference of the circle should be written correctly. Also, while substituting the values in the expression, make sure that the values are orderly put without any mistakes. Do not take the value of the diameter of the wheel directly, first find the radius and then use it in the formula for the circumference of a circle.