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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
\[\theta = 25^\circ = \left( 25 \times \frac{\pi}{180} \right) = \frac{5\pi}{36}\text{ radian }\]
We know:
\[\theta = \frac{\text{ Arc }}{\text{ Radius }}\]
\[ \Rightarrow \frac{5\pi}{36} = \frac{40}{\text{ Radius }}\]
\[ \Rightarrow \text{ Radius }= \frac{40}{\frac{5\pi}{36}}\]
\[ = \frac{40 \times 36 \times 7}{5 \times 22}\]
\[ = 91 . 64 m\]
So, the radius of the track should be 91.64 m.
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