Question

The radius of the wheel of the bus is 35 cm . How many rotations will the wheel complete by travelling 11 km?

Answer 1

Hint: The radius of the wheel is 35 cm and it is understood that the distance covered by one rotation is equal to the circumference of the wheel and it is given by $2\pi r$ units and since the radius and the total distance to be covered are given in different units we need to convert any one of them and then taking n to be the number of rotations we get n * distance covered by 1 rotation = 11 km and simplifying this we get the value of n

Complete step-by-step answer:
We are given that the radius of the wheel of the bus is 35 cm
We know that for one rotation the entire boundary of the wheel should touch the ground
Hence from this it is clear that the distance covered by one rotation is equal to the circumference of the wheel
Since the circumference of a circle is $2\pi r$units
Distance covered in one rotation = $2\pi r$
Now we are given that the total distance covered is 11 km
We are given the radius in centimetres and distance in kilometres
So lets convert the radius into kilometres before proceeding further
Hence to convert centimetre to kilometre we need to divide it by 100000
$ \Rightarrow \dfrac{{35}}{{100000}} = 0.00035km$
Now let n be the number of rotations taken to cover 11 km
Hence
$ \Rightarrow 11 = $ n * distance covered by 1 rotation
$
   \Rightarrow 11 = n*2*\dfrac{{22}}{7}*0.00035 \\
   \Rightarrow 11 = n*2*22*0.00005 \\
   \Rightarrow 11 = n*44*0.00005 \\
   \Rightarrow n = \dfrac{{11}}{{44*0.00005}} \\
   \Rightarrow n = \dfrac{1}{{4*0.00005}} \\
   \Rightarrow n = \dfrac{1}{{0.0002}} \\
   \Rightarrow n = 5000 \\
$
Hence we get that it takes 5000 rotations to cover 11 km.

Note: Many students tend to get confused whether to use perimeter or area.
We use the perimeter as the boundary only touches the road .
Whenever we are given quantities with different units we need to convert them to one common unit before proceeding with the calculations .