# A boy is cycling in such a way that the wheels of his bicycle are making 140 revolutions per minute.

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.

Solution:

Diameter of the wheel = 60 cm
​∴ Radius of the wheel = 30 cm

Circumference of the wheel $=2 \pi \mathrm{r}$

$=2 \times \frac{22}{7} \times 30$

$=\frac{1320}{7} \mathrm{~cm}$

Distance covered by the wheel in 1 revolution $=\frac{1320}{7} \mathrm{~cm}$

$\therefore$ Distance covered by the wheel in 140 revolutions $=\left(\frac{1320}{7} \times 140 \times \frac{1}{100}\right) \mathrm{m}$

$=\left(\frac{1320 \times 140}{7 \times 100} \times \frac{1}{1000}\right) \mathrm{km}=\frac{264}{1000} \mathrm{~km}$

Now,

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

$\therefore$ 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 $15.84 \mathrm{~km} / \mathrm{h}$.