Question

Suppose Eratosthenes’ results for Earth’s circumference were quite accurate. If the diameter of Earth is 12,740 km, what is the length of his stadium in kilometers?

Answer 1

The Results For Earth's Circumcised were quite accurate. the diameter of earth is 12,740 km, the length of the stadium would be 1,140 km. 

Answer 2

Length of one stadium = 0.1556 km

Step-by-step explanation:

We have the diameter of Earth = 12740 km

Thus, circumference (C) of Earth is

`=2\pi (Diameter)/(2) \\`

`=2* \pi * (12740)/(2)`

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 (
`\theta`) 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:

`(\theta )/(360)=(D)/(C)`

`=(7)/(360)=(5000 * S)/(40023.89)`

`=5000 * S = (7* 40023.89)/(360)`

`=S = (7* 40023.89)/(360*5000)`

S = 0.1556 km