Question

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

Answer 1

Step 1. Determine the circumference.

The diameter of the front and rear wheels are $80\mathrm{cm}\mathrm{and}2\mathrm{m}=200\mathrm{cm}$.

Find the circumference of the wheels:

$\begin{array}{rcl}{C}_1& =& \pi \times 80\mathrm{cm}\\ & \Rightarrow & {\mathrm{C}}_1=80\mathrm{\pi }\mathrm{cm}\end{array}$

$\begin{array}{rcl}{C}_2& =& \pi \times 200\mathrm{cm}\\ & \Rightarrow & {\mathrm{C}}_2=200\mathrm{\pi }\mathrm{cm}\end{array}$

So, the circumference of the front and rear wheels are $\begin{array}{l}80\mathrm{\pi }\mathrm{cm}\mathrm{and}200\mathrm{\pi }\mathrm{cm}\end{array}$.

Step 2 . Determine the number of revolutions of therear wheels.

The number of revolutions made by the front wheels is $1400$.

So, the distance covered by the front wheels is $1400\times 80\pi \mathrm{cm}$.

The distance covered by the front and rear wheels are the same and the number of revolutions is the distance covered divided by the circumference of the wheel.

Find the number of revolutions:

$\begin{array}{rcl}\frac{1400\times 80\pi \mathrm{cm}}{200\pi \mathrm{cm}}& =& \frac{1400\times 80}{200}\\ & \Rightarrow & \frac{1400\times 80\pi \mathrm{cm}}{200\pi \mathrm{cm}}=560\end{array}$

So, the number of revolutions made by the rear wheels is $560$.