The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Solution:

Distance traveled by the wheel in one revolution is the circumference of the wheel.

The diameter of the wheel of the car = 80 cm.

The radius of the wheel of the car = 40 cm

Distance travelled after 1 revolution = Circumference of the wheel

Circumference of the wheel = 2πr

= 2π (40) = 80π cm 

Thus, Distance traveled in 1 revolution = 80π ----------- (1)

Speed of car = 66 km/hour

Converting the speed into cm/min

= (66 × 100000)/60 cm/min

= 110000 cm/min

Distance traveled by car in the duration of 10 minutes

= 110000 × 10 [Since, Distance = Speed × Time]

= 1100000 cm --------- (2)

Let the number of revolutions of the wheel of the car be equal to 'n'.

n × Distance traveled in 1 revolution = Distance traveled in 10 minutes

n × 80π = 1100000 [From equation (1) and (2)]

n = (1100000 × 7)/(80 × 22)

= 35000/8

= 4375

Hence, each of the wheels of the car will make 4375 revolutions.

☛ Check: NCERT Solutions Class 10 Maths Chapter 12

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Video Solution:

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 4

Summary:

Each wheel of the car makes 4375 revolutions in 10 minutes if the wheels of the car are of diameter 80 cm each and the car is traveling at a speed of 66 km per hour.

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