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The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions

Solution:

Given, the diameter of front and rear wheels of a tractor are 80 cm and 2 m.

We have to find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

Number of revolutions = total distance / distance covered in one revolution

Distance covered in one revolution = 2πr

Given, diameter of front wheel, 2r = 80 cm

Distance covered in one revolution by the front wheel = 80π

Given, diameter of rear wheel, 2r = 2 m

1 m = 100 cm

So, diameter of rear wheel, 2r = 200 cm

Distance covered in one revolution by the rear wheel = 200π

Given, total number of revolutions by front wheel = 1400

So, total distance covered by front wheel = number of revolutions × distance covered in one revolution

= 1400(80π)

= 112000π cm

Let the number of revolutions by the rear wheel be c

Distance travelled by rear wheel = number of revolutions × distance covered in one revolution

= c × 200π

Both the wheels travel the same distance.

So, 112000π = c × 200π

112000 = c × 200

c = 112000/200

c = 1120/2

c = 560

Therefore, the number of revolutions made by the rear wheel is 560.

✦ Try This: The diameters of front and rear wheels of a truck are 90 cm and 95 m respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1600 revolutions.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 2

The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions

Summary:

The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. The number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions is 560

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