Question

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Answer 1

Hint: We will first find the circumference of the wheels in meters and then find the speed to car in meter / minute. Then we will just find the distance covered by car in 10 minutes and divide that by the circumference of the wheel to get the number of revolutions.

Complete step-by-step answer:
Since, we are given the diameter of the wheels to be 80 cm.
We know that 1 m = 100 cm.
So, 100 cm = 1 m.
So, \[1cm = \dfrac{1}{{100}}m\].
Hence, \[80cm = \dfrac{1}{{100}} \times 80m = 0.8m\]
We also know that $Radius = \dfrac{{Diameter}}{2}$
So, the radius of wheels will be $\dfrac{{0.8}}{2}m = 0.4m$.
Circumference is given by $2\pi r$, where r is the radius.
Hence, Circumference of the wheel will be $2 \times \pi \times 0.4m = 0.8\pi m$.
Now, let us look at the speed of the car which is given to be 66 km per hour.
This means in 1 hour, the car covers = 66 km
This can be written as in 60 minutes, the car covers = $(66 \times 1000)m = 66000m$
So, in 1 minute the car will cover = $\dfrac{{66000}}{{60}}m = 1100m$.
Hence, in 10 minutes, it will cover = $(1100 \times 10)m = 11000m$.
So, the number of revolutions will be given by the resultant of the distance covered by the car in 10 minutes and the circumference of the wheel.
Hence, Number of revolutions = $\dfrac{{11000}}{{0.8\pi }}$.
Putting in the value of $\pi $, we will get:-
Number of revolutions = $\dfrac{{11000 \times 7}}{{0.8 \times 22}} = 4375$.

Hence, each wheel makes 4375 rotations.

Note: The students must wonder why we consider the circumference of the wheel only, not any other value? Now, since the revolutions made by a wheel will be the number of times the wheel completely traces the road to cover the distance and obviously, only the boundary of the wheel is responsible for the revolutions. Hence, we needed to find the circumference of the wheel.
Since, it is not mentioned in the question to use any particular value of $\pi $, you may use either $\dfrac{{22}}{7}$ or 3.14 depending on your comfort. But using $\dfrac{{22}}{7}$ will give you a more accurate answer.