## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 35 of Exercise 18B

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35
##### The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers in 800 revolutions.

Given diameter of front wheel = d = 80 cm

so, Radius of front wheel = r = d/2 = 80/2 = 40 cm

Diameter of rear wheel = D = 2 m = 200 cm

Distance covered by wheel in 1 revolution = Circumference of wheel

Distance covered by front wheel = 2πr = 2π(40)

Distance covered by front wheel = 80π

Distance covered by front wheel in 800 revolutions = 80π×800

Distance covered by front wheel in 800 revolutions = 6400π eqn1

Similarly

Distance covered by rear wheel = 2πR = 2π(100)

Distance covered by rear wheel = 200π eqn2

Let the number of revolutions made by rear wheel to cover 6400π cm be “x”

(x)×200π = 6400π (from eqn1 and eqn2)

x = 64000/200

x = 320

Number of revolution made by rear wheel to cover the distance covered by front wheel in 800 revolutions is 320.

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