# The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute.

Question:

The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine its speed in kilometres per hour. [Use π = 22/7]

Solution:

It is given that the diameter of the wheel is $90 \mathrm{~cm}$.

$\therefore$ Radius of the circular wheel, $\mathrm{r}=\frac{90}{2}=45 \mathrm{~cm}$.

$\therefore$ Perimeter of the wheel $=2 \times \pi \times \mathrm{r}=2 \times \frac{22}{7} \times 45=282.857 \mathrm{~cm}$

It means the wheel travels $282.857 \mathrm{~cm}$ in a revolution.

Now, it makes 315 revolutions per minute.

$\therefore$ Distance travelled by the wheel in one minute $=315 \times 282.857=89100 \mathrm{~cm}$

$\therefore$ Speed $=89100 \mathrm{~cm}$ per minute $=\frac{89100 \mathrm{~cm}}{1 \text { minute }}$

Now, we need to convert it into kilometers per hour.

$\therefore \frac{89100 \mathrm{~cm}}{1 \text { minute }}=\frac{89100 \times \frac{1}{100000} \text { kilometer }}{\frac{1}{60} \text { hour }}$

$=\frac{89100}{100000} \times \frac{60}{1} \times \frac{\text { kilometer }}{\text { hour }}$

$=53.46$ kilometers per hour