Question

The number of revolutions made by a wheel of diameter 56 cm in covering a distance of 1.1 km is (Use $\pi ={\displaystyle \frac{22}{7}}$)
1) 31.25
2) 56.25
3) 625
4) 62.5

Answer 1

Hint: We will begin by determining the radius of the wheel from the given diameter. The next step is to convert the units of distance covered to cm, as the units must be the same. The total distance covered in one revolution will be equal to the perimeter of the wheel. Finally, to find the total number of revolutions, divide the total distance by distance covered in one revolution.

Complete step-by-step answer:
We are given that the diameter of the wheel is 56 cm.
We will find the radius of the wheel using the relation, $\text{Radius}={\displaystyle \frac{\text{Diameter}}{2}}$
Hence, the radius of the given wheel is calculated as, $\text{Radius}={\displaystyle \frac{56}{2}}$ = 28 cm
Now, we are given that the total distance covered by the wheel is 1.1 km. But, we have a radius in cm.
So, convert 1.1 km into cm by multiplying 1.1 by 1,00,000 as 1km=1,00,000cm
Hence, we can write 1.1. km as $1.1\times 1,00,000$=1,10,000 cm
The distance covered in one revolution is equal to the perimeter of the wheel.
We can calculate the perimeter of the wheel using the formula, $2\pi r$, where $r$ is the radius of the circle.
Use $\pi ={\displaystyle \frac{22}{7}}$ and $r=28$ cm to find the perimeter.
$2\left({\displaystyle \frac{22}{7}}\right)\left(28\right)=176\text{ cm}$
Finally, we will determine the total number of revolutions by dividing the total distance by distance covered in one revolution.
${\displaystyle \frac{1,10,000}{176}}=625$
Hence, the total number of revolutions is 625.
Therefore, option C is the correct answer.

Note: Many students forget to convert diameter into radius and end up getting wrong answers. Also, it is important to make the units the same in this question. If we will use distance covered as 1.1 km with the radius as 28cm, then it will give the wrong answer. Also, use the value of $\pi ={\displaystyle \frac{22}{7}}$ as given in the question instead of 3.14 to avoid unnecessary calculations.