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.

Question

Philoid · Accepted Answer

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.