The radius of the wheel of a vehicle is 42 cm. How many revolutions will it complete in a 19.8-km-long journey?

In one revolution a wheel will cover a distance equal to its circumference, so in order to find the number of revolutions we have to first calculate the circumference of the wheel and then divide it with the total distance covered to find out the total number of revolutions

Given radius of wheel = r = 42 cm

Circumference of wheel = 2πR where R = radius of the wheel

= 2π(42) (putting value of r)

Therefore distance covered in one revolution = 264 cm

Total distance covered = 19.8 km = 1980000 cm

Total number of revolutions = n

Distance covered on 1 revolution ×no. of revolutions = Total distance

264×n = 1980000

⇒ n = 7500

Total number of revolutions is 7500.

30