Question

The wheels of a car are of diameter $80\text{cm}$ each. How many complete revolutions does each wheel make in $10\text{minutes}$ when the car is travelling at a speed of $\text{66 km/h}$ ?

Answer 1

The diameter of the wheel of the car $=80\text{cm}$

So the Radius (r) of the wheel of the car $=40\text{cm}$

The formula of the circumference of circle C = 2πr.

The Circumference of wheel $=2\mathrm{\pi r}=2\mathrm{\pi }\left(40\right)=80\mathrm{\pi }\mathrm{cm}$

Speed of car $=66\text{km/h}$

Converting $\mathrm{km}$ into $\mathrm{cm}$ we get,

Distance covered by the car in $1\text{hr}$$=66\times {10}^5\text{cm}$

In $10$ minutes, the distance covered will be $=\frac{66\times {10}^5\times 10}{60}=110000\text{cm/s}$

Speed(cm/min)$=110000\text{cm/s}$

Distance travelled by the car in $10$ minutes $=110000\times 10=1100000\text{cm}$

Let the number of revolutions of the wheel of the car be $\mathrm{R}$.

So, equating it now

We get, $\text{R×}$ Distance travelled in $1$ revolution $=$ Distance travelled in $10$ minutes

$$\begin{gathered} 80\mathrm{\pi R}=1100000 \\ 80\times \frac{22}{7}\times \mathrm{R}=1100000 \\ \mathrm{R}=1100000\times \frac{7}{22}\times \frac{1}{80}=4375 \end{gathered}$$

Hence number of revolutions are $4375$