In Centesimal system of surveying 1 circumference is in how many grades?
400
Understanding the Centesimal System in Surveying
The question asks about the number of grades that make up one complete circumference in the Centesimal system of surveying. The Centesimal system is a way of measuring angles, often used in surveying and some European countries.
In angular measurement systems, a full circle or circumference is typically divided into a specific number of units. Common systems include Degrees, Radians, and Grades (Centesimal system).
Divisions in the Centesimal System
The Centesimal system divides angles based on powers of 100. The main unit is the 'grade'. Here's how it works:
- A right angle (a quarter of a circle) is divided into 100 grades (g).
- Each grade is divided into 100 centigrades (c).
- Each centigrade is divided into 100 milligrades (cc).
So, 1 grade = 100 centigrades, and 1 centigrade = 100 milligrades. This makes calculations easier with decimal numbers.
Circumference in the Centesimal System
A complete circle or circumference consists of four right angles.
- Full Circle = 4 Right Angles
Since, in the Centesimal system, one right angle is equal to 100 grades, we can calculate the number of grades in a full circle:
\( \text{Number of grades in a circumference} = \text{Number of right angles in a circumference} \times \text{Number of grades in a right angle} \)
\( \text{Number of grades in a circumference} = 4 \times 100 \text{ grades} \)
\( \text{Number of grades in a circumference} = 400 \text{ grades} \)
Therefore, one circumference in the Centesimal system of surveying is equal to 400 grades.
| System | Units in a Right Angle | Units in a Full Circle (Circumference) |
|---|---|---|
| Degrees (Sexagesimal) | \( 90^\circ \) | \( 360^\circ \) |
| Radians | \( \frac{\pi}{2} \) radians | \( 2\pi \) radians |
| Grades (Centesimal) | 100 grades (g) | 400 grades (g) |
Answer Derivation
Based on the calculation and the definition of the Centesimal system, a full circumference contains 400 grades.
Revision Table: Centesimal System Key Points
| Concept | Description in Centesimal System |
|---|---|
| Unit of Angle | Grade (g) |
| Subunits | Centigrade (c), Milligrade (cc) |
| Right Angle | 100 grades |
| Full Circle (Circumference) | 400 grades |
Additional Information: Converting Between Angular Units
It's often necessary to convert angles between different systems. Here are some common conversions based on a full circle:
- \( 360^\circ = 2\pi \) radians \( = 400 \) grades
From this, you can derive conversion factors:
- Degrees to Grades: \( \text{Grades} = \text{Degrees} \times \frac{400}{360} = \text{Degrees} \times \frac{10}{9} \)
- Grades to Degrees: \( \text{Degrees} = \text{Grades} \times \frac{360}{400} = \text{Grades} \times \frac{9}{10} \)
- Radians to Grades: \( \text{Grades} = \text{Radians} \times \frac{400}{2\pi} = \text{Radians} \times \frac{200}{\pi} \)
- Grades to Radians: \( \text{Radians} = \text{Grades} \times \frac{2\pi}{400} = \text{Grades} \times \frac{\pi}{200} \)
These conversion factors are useful in surveying and other fields where angular measurements are used in different systems.
Important Questions from Compass Surveying and Theodolite
What is the difference of longitude between two places C and D from the following longitudes ?
1. Longitude of C = 46° W
2. Longitude of D = 64° W
Arrange the order of permanent adjustment of a theodolite.
1) Plate level test
2) Cross- hair ring test
3) Bubble tube adjustment test
4) Spire test
5) Collimation in azimuth test
6) Vertical circle test
Isogonic lines are the lines having the same _______.
Which one of the following statements is correct?
Which optical element's movement within a telescope typically enables internal focusing while maintaining a constant physical length of the instrument?
