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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?
Given: The wheels of a car are of diameter $80\ cm$ each. The car is travelling at a speed of $66$ km per hour in $10$ minutes.
To do: To find the number of revolution completed by the wheel in $10$ minutes.
Solution:
As given, diameter of the wheel$=80\ cm$
$\therefore$ Radius of the wheel $r=\frac{Diameter}{2}=\frac{80}{2}=40\ cm$
Circumference of the wheel$=2\pi r=2\times\frac{22}{7}\times40=251.42\ cm=2.51\ m$
Speed of the car$=66\ km/h$
Time to travel by the car$=10$ minutes$=\frac{10}{60}=\frac{1}{6}$ hour
$\therefore$ Distance travelled by the car$=speed\times time=66\times\frac{1}{6}=11\ km=11000\ m$
Let $n$ be the number of revolutions completed by the wheel in $10$ minutes.
$\therefore n\times2.51=11000$
$\Rightarrow n=\frac{11000}{2.51}=4375.49$
Thus, each wheel will make around $4375$ revolutions in $10$ minutes.