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30 Jun 2019, 23:57
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (03:04) correct
39%
(02:59)
wrong
based on 260
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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%
1. 1%-16%
2. 15%-75%
3. 84%-99%
4. 523%-621%
5. 98896%-118121%
01 Jul 2019, 00:05
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ArtyomYom
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%
1. 1%-16%
2. 15%-75%
3. 84%-99%
4. 523%-621%
5. 98896%-118121%
Given:
Ler = 252 000 st.
1st = 160 m.
2ed = 185 m.
Lea = 24 900 mil.
1 mil = 1,6
Approach:
Let's translate this in km
Eratosthenes length = (252000)/(160*1000) = 252*160 = 25200*1,6
Real = 24900*1,6
As we can see the difference is small between 25200*1,6 and 24900*1,6
((25200*1,6)-(24900*1,6))/24900 ~ 1%
Answ A
03 Jul 2019, 19:34
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The fact that the answer options are ranges, should make it evident that, approximation is the way to go in this question.
Since stadion to metre conversion is provided, firstly, we will have to convert the circumference in miles to circumference in kilometres.
To keep things simple, instead of 24,900 miles, let’s take the circumference of the earth as 25000 miles. But while converting it to kilometres, let’s multiply it by 1.6 rather than 1.61, to account for the 100 mile increase in the circumference of the earth.
25000 * 1.6 = 40000 kilometres.
1 kilometre = 1000 metres. Therefore, circumference of earth = 4,00,00,000 metres.
Also, instead of 159.4, let’s use 160. So, 252000 stadia = 252000 * 160 = 4,03,20,000 metres. The error is 3,20,000 which is approximately 1% of 4,00,00,000.
252000 stadia * 185 = 4,66,20,000. The error is 66,20,000 which is approximately slightly more than 15%.
So, the error range is between 1% to 15%.
The correct answer option is A.
Hope this helps!
Since stadion to metre conversion is provided, firstly, we will have to convert the circumference in miles to circumference in kilometres.
To keep things simple, instead of 24,900 miles, let’s take the circumference of the earth as 25000 miles. But while converting it to kilometres, let’s multiply it by 1.6 rather than 1.61, to account for the 100 mile increase in the circumference of the earth.
25000 * 1.6 = 40000 kilometres.
1 kilometre = 1000 metres. Therefore, circumference of earth = 4,00,00,000 metres.
Also, instead of 159.4, let’s use 160. So, 252000 stadia = 252000 * 160 = 4,03,20,000 metres. The error is 3,20,000 which is approximately 1% of 4,00,00,000.
252000 stadia * 185 = 4,66,20,000. The error is 66,20,000 which is approximately slightly more than 15%.
So, the error range is between 1% to 15%.
The correct answer option is A.
Hope this helps!
