Question

A boy is cycling in such a way that the wheels of his bicycle are making 140 revolutions per minute. If the diameter of a wheel is 60 cm, calculate the speed (in km/h) at which the boy is cycling.

Answer 1

Diameter of the wheel = 60 cm
​∴ Radius of the wheel = 30 cm
​Circumference of the wheel = $2\mathrm{\pi r}$
$$\begin{gathered} =2\times \frac{22}{7}\times 30 \\ =\frac{1320}{7}\mathrm{cm} \end{gathered}$$
Distance covered by the wheel in 1 revolution = $\frac{1320}{7}\mathrm{cm}$
∴ Distance covered by the wheel in 140 revolutions = $\left(\frac{1320}{7}\times 140\times \frac{1}{100}\right)\mathrm{m}$
$=\left({\displaystyle \frac{1320\times 140}{7\times 100}}\times {\displaystyle \frac{1}{1000}}\right)\mathrm{km}=\frac{264}{1000}\mathrm{km}$

Now,
Distance covered by the wheel in 1 minute = Distance covered by the wheel in 140 revolutions = $\frac{264}{1000}\mathrm{km}$

∴ Distance covered by the wheel in 1 hour = $\frac{264}{1000}\times 60=15.84\mathrm{km}/\mathrm{h}$

Hence, the speed at which the boy is cycling is 15.84 km/h.