question: How is the area of a country calculated given that the Earth is a sphere?
comment: The earth is spherical but that doesn't mean the land doesn't sit flush on its surface). So in that respect they can measure the area of a country or the area of the earth's surface or the area of anything on the earth because the same general geometry rules apply there.
passages: Percentage figures for arable land, permanent crops land and other lands are all taken from CIA World Factbook as well as total land area figures (note that total area of a country is a sum of total land area and total water area). All other figures, including total cultivated land area, are calculated on the basis of this mentioned data.
   In comparison, based on a world population of seven billion, the world's inhabitants, as a loose crowd taking up ten square feet (one square metre) per person (Jacobs Method), would occupy a space a little larger than Delaware's land area.
  
  Section::::Biological population densities.:Countries and dependent territories.
  
  The Gaza Strip (exclave of Palestine) has a population of 1.85 million and a population density of 5,046 pop/km.
  
  Section::::Biological population densities.:Other methods of measurement.
   The United States Department of Agriculture (USDA) Economic Research Service measures distance by dividing the country into multiple 0.5 km square grids. The distance from the geographic center of each grid to the nearest grocery store gauges food accessibility for the people living in that grid. Health Canada divides areas into buffer zones with people's homes, schools or workplaces as the center. The Euclidean distance is the shortest distance between the two points of interest, which is measured for gaining food access data.
   Section::::Principal UM suites at the Met Office.:North Atlantic and European model - Retired.
  
  The Met Office's North Atlantic and European model (NAE) model had 70 levels with a 12 km resolution. It is run out to 48 hours from start. Because the UK is at a northern latitude the computer transposes the model area to an equatorial location so the grid points give an area that is more square. This reduces the load on the model, allowing it to run more quickly. The model is kept close to the real atmosphere using 4D-Var data assimilation of observations.
   In the map (figure 1), which uses the AA scheme, we see that Honolulu is in grid zone 4Q, and square FJ. To give the position of Honolulu with 100 km resolution, we write 4QFJ.
  
  Section::::Numerical location.
   In summary, local variations in terrain prevent defining a single "precise" radius. One can only adopt an idealized model. Since the estimate by Eratosthenes, many models have been created. Historically, these models were based on regional topography, giving the best reference ellipsoid for the area under survey. As satellite remote sensing and especially the Global Positioning System gained importance, true global models were developed which, while not as accurate for regional work, best approximate the Earth as a whole.
  
  Section::::Fixed radius.
   BULLET::::- For 1:50,000 maps, the grid lines are 2 cm apart. Each square on the map is 2 cm by 2 cm (4 cm) and represents 1 km on the surface of the earth.
  
  BULLET::::- For 1:25,000 maps, the grid lines are 4 cm apart. Each square on the map is 4 cm by 4 cm (16 cm) and represents 1 km on the surface of the earth.
  
  In each case, the grid lines enclose one square kilometre.
  
  Section::::Examples of areas of 1 square kilometre.:Medieval city centres.
   Sources for population estimates and land area definitions are coded by letter in the cited report, respectively.
  
  The projected year (2017) population estimate is further calculated from the base year population estimate using population growth rate based upon the United Nations population growth rate with some exceptions.
   The simplest model for the shape of the entire Earth is a sphere. The Earth's radius is the distance from Earth's center to its surface, about . While "radius" normally is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth".
   The abovementioned larger and smaller sizes of the Earth were those used by Claudius Ptolemy at different times, 252,000 stadia in his "Almagest" and 180,000 stadia in his later "Geographia". His midcareer conversion resulted in the latter work's systematic exaggeration of degree longitudes in the Mediterranean by a factor close to the ratio of the two seriously differing sizes discussed here, which indicates that the conventional size of the earth was what changed, not the stadion.
  
  Section::::Ancient India.
   On sloping ground, the "above ground" reference point is usually taken as the highest point on the ground touching the trunk, but some use the average between the highest and lowest points of ground. If the DBH point falls on a swelling in the trunk it is customary to measure the girth below the swelling at the point where the diameter is smallest. Other ambiguous settings for determining the exact place where to measure the diameter is given in Dahdouh-Guebas & Koedam (2006).
   From 1958, a number of town maps at scales of 1:5,000 or 1:10,000 were also made, initially on the Gauss-Krϋger projection, but after 1970 on a stereographic projection. More than 100 such sheets have been produced. There is also a street map of Bucharest in four sheets at 1:15,000 derived from larger scale surveys, which is revised annually.
   Whether the US or China is the third largest country by total area depends on two factors: (1) The validity of China's claim on Aksai Chin and Trans-Karakoram Tract. Both these territories are also claimed by India, so are not counted; and (2) How US calculates its own surface area. Since the initial publishing of the World Factbook, the CIA has updated the total area of United States a number of times.
  
  Section::::General characteristics.
   In the United States, OSM uses Landsat 7 satellite imagery, Prototype Global Shorelines from NOAA, and TIGER from the Census. In the UK, some Ordnance Survey OpenData is imported, while Natural Resources Canada's CanVec vector data and GeoBase provide landcover and streets.
   Treated as a sphere, determining Earth's circumference would be its single most important measurement (Earth actually deviates from a sphere by about 0.3% as characterized by flattening).
  
  Section::::History of calculation.
   The countries with the highest border/area ratios are some of the smallest, non-island, nations of the world, such as Vatican City, Monaco and San Marino.
  
  Many island nations, lack any land borders and thus have a border/area ratio of zero.
  
  Section::::See also.
  
  BULLET::::- How Long Is the Coast of Britain?
  
  BULLET::::- List of countries by area
  
  BULLET::::- List of countries and territories by maritime boundaries
  
  BULLET::::- List of countries that border only one other country
  
  BULLET::::- List of land borders by date of establishment
  
  BULLET::::- List of divided islands
  
  BULLET::::- List of island nations
   Since the spherical shape was the most widely supported during the Greek Era, efforts to determine its size followed. Aristotle reported that mathematicians had calculated the circumference of the Earth (which is slightly over 40,000 km) to be 400,000 stadia (between 62,800 and 74,000 km or 46,250 and 39,250 mi) while Archimedes stated an upper bound of 3,000,000 stadia (483,000 km or 300,000 mi) using the Hellenic stadion which scholars generally take to be 185 meters or of a geographical mile.
  
  Section::::Hellenic world.:Hellenistic world.
   The Isle of Wight (), an island off the south coast of mainland England, is commonly used to define smaller areas. It has sometimes been used in attempts to examine whether a certain amount of a given object or group would fit in a space its size; in 2018, it was estimated that approximately 2.6 billion people could fit on the Isle of Wight, at a population density of six people per square metre.
  
  In Denmark, the island of Bornholm (588 square kilometers) is often used to describe the size of an area.
   The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length and width , the formula for the area is:
  
  That is, the area of the rectangle is the length multiplied by the width. As a special case, as in the case of a square, the area of a square with side length is given by the formula:
   Section::::Geodesics on an ellipsoid of revolution.:Area of a geodesic polygon.
  
  A "geodesic polygon" is a polygon whose sides are geodesics. The area of
  
  such a polygon may be found by first computing the area between a
  
  geodesic segment and the equator, i.e., the area of the quadrilateral
  
  area is known, the area of a polygon may be computed by summing the
  
  contributions from all the edges of the polygon.
  
  Here an expression for the area of 
  
  is developed following . The area of any closed
  
  region of the ellipsoid is
  
  where is an element of surface area and 
   A morgen ("morning" in Dutch and German) was approximately the amount of land tillable by one man behind an ox in the morning hours of a day. This was an official unit of measurement in South Africa until the 1970s, and was defined in November 2007 by the South African Law Society as having a conversion factor of 1 Morgen = . This unit of measure was also used in the Dutch colonial province of New Netherland (later New York and parts of New England).
  
  Section::::Area.:Countries, regions, and cities.
   Most basic formulas for surface area can be obtained by cutting surfaces and flattening them out. For example, if the side surface of a cylinder (or any prism) is cut lengthwise, the surface can be flattened out into a rectangle. Similarly, if a cut is made along the side of a cone, the side surface can be flattened out into a sector of a circle, and the resulting area computed.
   If we are willing to accept a possible error of 0.5%, we can use formulas of spherical trigonometry on the sphere that best approximates the surface of the earth.
  
  The shortest distance along the surface of a sphere between two points on the surface is along the great-circle which contains the two points.
  
  The great-circle distance article gives the formula for calculating the distance along a great-circle on a sphere about the size of the Earth. That article includes an example of the calculation.
  
  Section::::Spherical-surface formulae.:Tunnel distance.
   A wedge prism can be used to quickly estimate the basal area per hectare. To find basal area using this method, simply multiply your BAF (Basal Area Factor) by the number of "in" trees in your variable radius plot. The BAF will vary based on the prism used, common BAFs include 5/8/10, and all "in" trees are those trees, when viewed through your prism from plot centre, that appear to be in-line with the standing tree on the outside of the prism.
  
  Section::::Worked example.
   During the 1874-77 survey by the Survey of India under E. C. Ryall, I. S. Pocock set up a plane table at c.22050' on the West flank of Abi Gamin.
  
raw_presuppositions: Area can only be calculated on flat surfaces. A country is considered spherical.
raw_corrections: You can measure the area of a country on Earth's surface even though Earth is spherical. A country sits flush on the surface of the Earth's spherical surface.