A rail road curve is to be laid out on a circle.
Question:

A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?

Solution:

Length of the arc = 40 m

$\theta=25^{\circ}=\left(25 \times \frac{\pi}{180}\right)=\frac{5 \pi}{36}$ radian

We know,

$\theta=\frac{\text { Arc }}{\text { Radius }}$

$\Rightarrow \frac{5 \pi}{36}=\frac{40}{\text { Radius }}$

$\Rightarrow$ Radius $=\frac{40}{\frac{5 \pi}{36}}$

$=\frac{40 \times 36 \times 7}{5 \times 22}$

$=91.64 \mathrm{~m}$

So, the radius of the track should be 91.64 m.