Answer:
Length of one stadium = 0.1556 km
Explanation:
We have the diameter of Earth = 12740 km
Thus, circumference (C) of Earth is
[tex]=2\pi \frac{Diameter}{2} \\[/tex]
[tex]=2\times \pi \times \frac{12740}{2}[/tex]
C = 40023.89 km
Eratosthenes was a Greek polymath. He was the first to calculate the circumference of Earth. He had observed that at local noon on day of Summer Solstice, when Sun is overhead for the locations on Tropic of Cancer, a place named Syene had zero shadow day. Also on the same day the objects in Alexandria casts shadow. This proved that Earth is spherical and not flat. He went further and calculated the Sun angle ([tex]\theta[/tex]) for Alexandria by using a Rod (Gnomon). He found the angle to be about 7°. He also knew the distance (D) between Alexandria and Syene which was 5000 Stadia.
Lets say length of one stadia = S km
He used this data and simple concept of geometry as given below:
[tex]\frac{\theta }{360}=\frac{D}{C}[/tex]
[tex]=\frac{7}{360}=\frac{5000 \times S}{40023.89}[/tex]
[tex]=5000 \times S = \frac{7\times 40023.89}{360}[/tex]
[tex]=S = \frac{7\times 40023.89}{360\times5000}[/tex]
S = 0.1556 km
