Question

17. The diameters of the front wheel and the rear wheel of an engine are 70 cm and 168 cm respectively. How many times the rear wheel should fully rotate in order to cover a distance for which the front wheel rotates 600 times ?
plz explain step by step​

Answer 1

250 Times

Step-by-step explanation:

Given:

Diameter of front wheel (d) = 70 cm

Diameter of rear wheel (D) = 168 cm

To Find:

Times of Rotation of rear will to cover the same distance for the rotation of front wheel in 600 times.

How to Solve ?

1. Analysing the question I get, Wheel rotation it's mean circumference. So we have to write circumference formula i.e 2πr [where r is Radius of circular object].

2. Assume a variable.

3. Form a equation.

4. Solve and get Answer.

Solution:

Front Wheel

d = 70 cm So, r = d/2 35 cm

Therefore, circumference = 2πr unit

= 2π × 35 cm

Distance covered by 600 times rotation,

= 2π × 35 × 600 cm

Rear Wheel

D = 168 cm So, R = D/2 84 cm

Therefore, circumference = 2πr unit

= 2π × 84 cm

let, Rear wheel rotate x time to cover the same distance by front wheel.

Distance covered by x times rotation,

= 2π × 84 × x cm

According to equation,

$2\pi \times 84 \times x = 2\pi \times 35 \times 600 \\ \\ \cancel{2\pi} \times 84x= \cancel{2\pi}\times 35 \times 600 \\ \\ \cancel{84}x = \cancel{35} \times 600 \\ \\ \cancel{12}x = 5 \times \cancel{600} \\ \\ x= 5 \times 50 \\ \\ x = 250$

Therefore, required no. of rotation by rear wheel is 250 times.

Answer 2

Answer:

250

Step-by-step explanation:

hope this helps. u can understand