Fundamentals of Surveying (FS) Practice Exam

By arc definition, the radius of a 1° curve is _____ ft.

1. 4000.00

2. 5729.58

3. 1000.00

4. 2500.00

The correct answer is: 5729.58

To determine the radius of a 1° curve in the context of surveying, the relationship between the curvature degree and the radius must be understood. The radius of a circular curve can be calculated using the formula: \[ R = \frac{D \cdot 180 \cdot r}{\pi} \] where: - \( R \) is the radius, - \( D \) is the degree of curvature (in this case, 1°), - \( r \) is the radius in feet for 1° of curvature, calculated at 100 feet. For a curve of 1°, the radius can be further simplified to approximately 5729.58 feet. This is derived from the fact that the length of a curve for 1° is roughly equal to \( \frac{100 \cdot 360}{2 \pi} \), which gives this radius value. Therefore, recognizing the relationship of degrees to the radius of curvature is essential. The correct option reflects this important relationship and understanding of how curves are defined in surveying, highlighting the mathematical underpinnings of circular curves. In contrast, the other options represent various radius measurements that do not align with the definition of a 1° curve.