Question

If the wheel of the bus is $90cm$ diameter makes $210$ revolutions per minute, then find the speed of the bus in $km/hr$, to the nearest integer.

Answer 1

Since the diameter of the wheel is $90cm$, then its radius is $45cm$.
In one revolution, the wheel covers the distance of one circumference.
Circumference of the circle $=2\pi r=2\times \pi \times 45$
Since the wheel makes $210$ revolutions in one minute, it makes $\frac{210}{60}=\frac{7}{2}$ revolutions in one second.
Total distance covered in one second $=$ No. of rotations in one second $\times$ circumference $=\frac{7}{2}\times 2\times \frac{22}{7}\times 45=990$ cm/s
$cm/s$ can be converted to $km/hr$ using the formula $cm/s$ $\times \frac{18}{500}=$ $km/hr$
Therefore

$990\times \frac{18}{500}=35.64$ km/hr

Thus, speed of bus is $36km/hr$