Maps

To solve this, we need to calculate the total number of cells required for the DEM. A 30 m spatial resolution means each cell represents an area of 30 m × 30 m. Step 1: Calculate the area of one cell.
The area of one cell is: Step 2: Determine the area of the topographic map.
The topographic map scale is 1:50,000, which means 1 unit on the map represents 50,000 units on the ground. We are given that 1 minute (of latitude) corresponds to 1.85 km, which is the length of one side of the map. Since 1 minute of latitude corresponds to 1.85 km, the length of the map in kilometers is 1.85 km. In meters, this is: Now, the area of the map is: Step 3: Calculate the total number of cells.
To cover the entire area of the map, the number of cells required is: Thus, the correct answer is (A) 855,625.

A map projection is the method by which the three-dimensional surface of the Earth is represented on a two-dimensional plane. Different types of projections are used depending on the purpose and the area of the Earth being represented. Step 1: Explanation of the options
- Option (A): A map projection is indeed a systematic representation of latitude and longitude lines on a plane. This is one of the basic methods of representing the Earth's surface, typically using a grid system.
- Option (B): A map projection represents the 3D shape of the Earth on a 2D plane. This is the most fundamental definition of map projection, where a spherical or ellipsoidal Earth is mapped to a flat surface.
- Option (C): The projection used can indeed depend on the location of the area on Earth. Different projections may be better suited to represent different parts of the world, e.g., cylindrical projections for equatorial regions, conic projections for mid-latitudes, etc.
- Option (D): This option is incorrect. Theodolite observations of horizontal angles do not directly relate to map projections. This refers to angle measurements in surveying, which is a separate concept from map projection. Thus, the correct answers are (A), (B), and (C).

To calculate the minimum ground distance that can be represented on the map, we need to understand the scale of the map. A 1 degree by 1 degree area corresponds to a specific ground distance.
One degree of latitude corresponds to approximately 111 km on the ground (the value may slightly vary depending on the location).
Thus, for a 1 degree by 1 degree area: Since the map covers a 1 degree by 1 degree area, the minimum ground distance represented on this map is .
However, if the map has a specific scale that indicates a finer resolution, the minimum ground distance that can be represented may be smaller. The minimum ground distance is therefore 62.5 m when rounded to two decimal places.