Question

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed per hour with which the boy is cycling.

Answer 1

​​We have:
The diameter of the wheel = 60 cm
Distance covered by the wheel in 1 revolution = Circumference of the wheel
∴ Distance covered by the wheel in 1 revolution = $\mathrm{\pi d}=\left(\frac{22}{7}\times 60\right)\mathrm{cm}.$
∴ Distance covered in 140 revolutions = $\left(\frac{22}{7}\times 60\times 140\right)\mathrm{cm}=\left(\frac{184800}{7}\right)\mathrm{cm}=26400\mathrm{cm}$.

Thus, the wheel covers 26400 cm in 1 minute. Then,
$$\begin{gathered} \mathrm{Speed}=\left(\frac{26400}{100}\times 60\right)\mathrm{m}/\mathrm{hr}=\left(264\times 60\right)\mathrm{m}/\mathrm{hr} \\ \Rightarrow \mathrm{Speed}=\left(\frac{264\times 60}{1000}\right)\mathrm{km}/\mathrm{hr}=15.84\mathrm{km}/\mathrm{hr}. \end{gathered}$$
The speed with which the boy is cycling is 15.84 km/hr. ​