In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be

BTGmoderatorDC wrote: ↑

Tue Dec 29, 2020 4:19 pm

In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 159.4 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,900 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest to

1. 1%-16%
2. 15%-75%
3. 84%-99%
4. 523%-621%
5. 98896%-118121%


OA A

Solution:

Case 1. If 1 stadion = 159.4 meters, then the circumference of the Earth is 252,000 x 159.4 = 40,168,800 meters, which is 40,168.8 km or 40,168.8/1.61 ≈ 24,950 miles.

Case 2. If 1 stadion = 185 meters, then the circumference of the Earth is 252,000 x 185 = 46,620,000 meters, which is 46,620 km or 46,620/1.61 ≈ 28,957 miles.

Using the Case 1 measurement, we see that the circumference of the Earth is off by approximately 50 miles, and using the Case 2 measurement, we see that the circumference is off by approximately 4,057 milles. By looking at the given choices, we see that answer choice 1 is the best approximation of the error in Eratosthenes' calculation of the circumference of the Earth (notice that 50 mies is actually less than 1% of 24,900 miles and 4,057 miles is more than 10% but less than 20% of 24,900 miles).

Answer: 1