A bus has wheels of diameter 0.7 m. How many times must a wheel of the bus rotate for covering the distance of 22 km between two towns?

Given: Diameter of the wheels of the bus = 0.7 m

⇒ Radius of the wheels of the bus, r = diameter/2 = 0.7/2 = 0.35 m

⇒ r = 0.35 m

We have

We need to find circumference of the wheels that will tell us about the distance it covers in 1 rotation.

Circumference of a circular wheel is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

If the circumference of the wheel = 2.2 m

Then, distance covered by the wheel in 1 rotation = 2.2 m

We know, 1 m = 0.001 km

⇒ 2.2 m = 2.2 × 0.001 = 2.2 × 10^-3 km

⇒ distance covered by the wheel in 1 rotation = 2.2 × 10^-3 km

Or

Rotations covered in 2.2 × 10^-3 km = 1

⇒ Rotations covered in 1 km = 1/(2.2 × 10^-3)

⇒ Rotations covered in 22 km = 22/(2.2 × 10^-3) = 10000

Thus, the wheels of the bus rotate 10,000 times for covering a distance of 22 km between two towns.