If the diameter of a car wheel is 28 cm, how many times will the wheel rotate in a journey of 11 km ?

Given:

Diameter of wheel = 28 cm

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

= $\dfrac{28}{2}$ cm

= 14 cm

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

$2 \times \dfrac{22}{7} \times 14\\[1em] = \dfrac{44}{7} \times 14\\[1em] = \dfrac{616}{7}\\[1em] = 88 \text{ cm}$

Let a be the number of revolutions.

Total distance = 11 km

= 11 x 1,00,000 cm

= 11,00,000 cm

Distance traveled by wheel in a revolutions = circumference of the wheel x a

⇒ 11,00,000 = 88 x a

⇒ a = $\dfrac{11,00,000}{88}$

⇒ a = 12,500 revolutions

Hence, the wheel rotates 12,500 times during a journey of 11 km.