Respuesta :
There are three theoretical indicators of the compactness of an area.
*the boundary-circumference ratio (B/C)
*the area-boundary ratio (A/B)
*the actual area-area of the inscribing circle (A/A)
Let’s use the boundary-circumference ratio to measure Ethiopia’s degree of compactness or index of compactness. In the ratio, circumference is based on an inscribing circle that touches the north, south, east and west boundaries of Ethiopia described earlier in the Absolute(Astronomical) Location section.
Index of compactness = Boundary Length/Circumference of the Inscribing Circle
and r is not given, we have to find it.
The inscribing circle is the circle drawn through the extreme points on the boundary of Ethiopia. The radius is obtained by taking half the length of the distance between the astronomical extremes of west and east of Ethiopia i.e., 48°E – 33°E = 15°/2 = 7°30’ (this is radius of the inscribing.
Then, change the obtained length (7°30') into kilometers:
1°= 110.5 km
7°30'× 110.5 km = 828.75 km
Therefore, index of compactness = 52601/2*3.14*828.75
= 1.01
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