Question

How many times A wheel of radius 28 cm must rotate to go 352 m?

Answer 1

Hint: Here, we will proceed by calculating the circumference of the given wheel which is equal to the distance covered by the wheel in one rotation. Finally, we will evaluate the total number of rotations taken to cover 352 m.

Complete step-by-step answer:
Let us consider a wheel A of radius 28 cm. Let us assume the number of rotations required by wheel A to cover 352 m distance be n.
Total distance covered, d = 352 m
As we know that the circumference of any circle represents the length of the outer boundary of the circle and the circumference of any circle having radius r is given by
Circumference of circle = $2\pi r$
The radius of the given wheel A, r = 28 cm
 Circumference of wheel A = $2\pi r = 2 \times \dfrac{{22}}{7} \times 28 = 176$ cm
Since, 1 cm = $\dfrac{1}{{100}}$ m
$ \Rightarrow $ Circumference of wheel A = $\dfrac{{176}}{{100}} = 1.76$ m
Also we know that the total distance covered in one rotation of a circular wheel of radius r is equal to the circumference corresponding to that wheel (i.e., $2\pi r$)
When a circular wheel of radius r takes n rotations, the total distance covered by the wheel will be equal to the product of the circumference of the wheel and the total number of rotations undertaken by the wheel
i.e., Total distance covered = (Circumference of the wheel)$ \times $(Total number of rotations)
$ \Rightarrow $ 352 =$1.76 \times n$
$ \Rightarrow n = \dfrac{{352}}{{1.76}} = 200$
Therefore, 200 total rotations are required for the given wheel A to go 352 m.

Note: In these type of problems, it is important to use the same unit for all the same physical quantities like here we have converted the unit of the circumference of the wheel A from centimetres (cm) to metres (m) because the distance given in the problem is also in metres (m).