 # The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Question:

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

Solution:

Let us find the distance covered by front wheel in 1400 revolutions.

We know that distance covered in n revolutions is equal to multiplication of number of revolutions and circumference of wheel.

$\therefore$ distance $=n \times 2 \times \pi \times r$

We have $r=80 \mathrm{~cm}$ therefore, we will convert it meters.

$\therefore r=0.8 \mathrm{~m}$

Now we substitute the values.

$\therefore$ distance $=1400 \times 2 \times \frac{22}{7} \times 0.8$

$\therefore$ distance $=7040$

Now we will calculate the number of revolutions that rear wheel will make to cover 7040 m.

$\therefore$ revolutions $=\frac{\text { Distance }}{\text { Circumference }}$

$\therefore$ revolutions $=\frac{7040}{2 \times \frac{22}{7} \times 2}$

$\therefore$ revolutions $=\frac{7040 \times 7}{88}$

$\therefore$ revolutions $=\frac{49280}{88}$

$\therefore$ revolutions $=560$

Therefore, the rear wheel will make 560 revolutions to cover $7040 \mathrm{~m}$.  