Question

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

Answer 1

Hint: To solve this question we will use the circumference of the circle which is given by C = 2πr, where r is the radius of the circle. Also, we will use the fact that the number for revolution made by the wheel is equal to the total distance travelled divided by the total number of revolutions.

Complete step-by-step solution -

Given that the wheel makes 1000 revolutions in covering a distance of 88 km, we have to find the radius of the wheel.
As the given distance is in kilometers, we will convert it into meters for further calculation. Therefore, the distance becomes,
We have 1km = 1000 m
Then this gives us 88 km = 88000m.
Therefore, the total distance travelled d = 88000m.
Now given that the wheel makes number of revolution = 1000
Therefore, the distance travelled by it in one revolution is obtained by dividing the total distance d in meters to the total number of revolutions.
Hence, the distance travelled by the wheel in one revolution becomes,
 \[\dfrac{88000}{1000}=88m\]
Therefore, it covers 88m in one revolution means that the circumference of the wheel is 88m.
Because the wheel is circular in shape therefore, the circumference is given by
Circumference C = 2πr, where r is the radius of the circle.
This gives that the circumference of the wheel is 88 is equal to 2πr, where r is the radius of the wheel.
Substituting the value of \[\pi =\dfrac{22}{7}\] in the above equation we get,

\[\begin{align}
  & 88=2\left( \dfrac{22}{7} \right)r \\
 & \Rightarrow ~88=\dfrac{44}{7}r \\
 & \Rightarrow r=\dfrac{7(88)}{44} \\
 & \Rightarrow r=14m \\
\end{align}\]

Therefore, we get the radius of the wheel as r = 14 m.

Note: The possibility of error in this question can be at the point where you have to convert the total distance travelled from kilometre to meter which is important because when we are doing calculations we have to convert all the given parameters in one single unit otherwise the answer would be wrong.