Question

How many times a wheel of radius 28 cm must rotate to go 352 m? $\left( Take\,\pi =\dfrac{22}{7} \right)$

Answer 1

Hint:Here we may first consider the number of revolutions to be ’n ’and then we may equate the total distance to the number of revolutions multiplied by the perimeter of the wheel because distance covered by the wheel in 1 revolution will be equal to the circumference of the wheel.

Complete step-by-step answer:
Radius of the wheel is given = 28 cm.
Since, we know that the formula for circumference of a circle is = $2\pi r$
So, using this formula circumference of the wheel is = $2\times \pi \times 28\,\,cm$
                                                                                              = $56\pi \,cm$
So, the circumference of the wheel is = $56\pi \,cm$ and it means that the distance covered by the wheel in 1 revolution is $56\pi \,cm$.
Now, let us consider the total number of revolutions that the wheel makes in covering 352 m be = x.
Since, the distance covered by the wheel in 1 revolution =$56\pi \,cm$.
Therefore, the distance covered by the wheel in x revolutions = $56\pi \times x\,\,cm$.
Since the radius of the wheel is given in cm and the total distance covered is given in m. So, we have to convert here the given distance in cm.
We know that 1m = 100 cm.
So, $352\,m\,=352\times 100\,cm$
Now we may equate the two distances to get the value of x.
So, $56\pi \times n=35200\,$
$56\times \dfrac{22}{7}\times x=35200$
 $8\times 22\times x=35200$
$x=\dfrac{35200}{8\times 22}$
So, $x = 200$

Hence, the total number of revolutions made by the wheel in covering 352 m is 200 revolutions.

Note: Here it should be noted that distance covered by the wheel in 1 revolution is always equal to the circumference of the wheel. There is a chance if they give distance in m we have to change into cm.Students should remember the formula of perimeter of circle and basic unit conversions for solving these types of questions.