A bicycle wheel, diameter 56 cm, is making 45 revolutions in every 10 seconds. At what speed, in kilo metre per hour, is the bicycle traveling ?

Given:

Diameter of wheel = 56 cm

Diameter of wheel in Kilometre = 0.00056 km

Radius = $\dfrac{\text{Diameter}}{2}$

= $\dfrac{0.00056}{2}$

= 0.00028 km

As we know, the circumference of the circle = 2πr

$= 2 \times \dfrac{22}{7} \times 0.00028\\[1em] = \dfrac{44}{7} \times 0.00028\\[1em] = \dfrac{0.01232}{7}\\[1em] = 0.00176 \text{ km}$

Distance traveled by wheel in 45 revolutions = Circumference of the wheel x 45

= 0.00176 x 45 km

= 0.0792 km

And, speed = $\dfrac{\text{Distance}}{\text{Time}}$

It is given that time taken by wheel = 10 sec = $\dfrac{10}{3600}$.

$\text{Speed} = \dfrac{0.0792 \times 3600}{10}\\[1em] = \dfrac{285.12}{10}\\[1em] = 28.512 \text{ km}/\text{hr}$

Hence, the speed = 28.512 km/hr.