Question

The diameter of a cart wheel is $1.4\mathrm{m}$. Find the distance to which the cart moves when wheel makes $1000$ revolutions.

Answer 1

Determine the distance covered in $1000$ revolutions.

The distance covered in $1$ revolution is equal to the circumference of a circle.

The radius of a circle is calculated by $r=\frac{d}{2}$ where $d$ represents the diameter of the circle.

So, $r=\frac{1.4}{2}=0.7\mathrm{m}$

The circumference of a circle $\left(C\right)$ is calculated by $C=2\mathrm{\pi r}$ where $r$ represents the radius of the circle.

$\begin{array}{rcl}C& =& 2\times \frac{22}{7}\times 0.7\\ & =& 4.4\mathrm{m}\end{array}$

The distance covered in $1$ revolution $=4.4\mathrm{m}$.

The distance covered in $1000$ revolution $=1000\times 4.4=4400\mathrm{m}$.

Convert $\mathrm{metre}$ into $\mathrm{km}$.

$\begin{array}{rcl}1\mathrm{m}& =& 0.001\mathrm{km}\\ & \Rightarrow & 4400\mathrm{m}=4400\times 0.001\\ & =& 4.4\mathrm{km}\end{array}$

Hence, the distance covered in $1000$ revolutions is $4.4\mathrm{km}$.