Question

The distance from Alexandria to Syene is about 500 miles. On the summer solstice the sun is directly overhead at noon in Syene. At Alexandria on the summer solstice, the sun is 1/50th of the circumference of the sky (about 7°) south of the zenith. Based on this information, what is the circumference of Earth? 6 25,000 miles 10 miles C. 3500 miles d. 3140 miles

Answer 1

Earth circumference is 25000 miles

correct option is 25,000 miles

Step-by-step explanation:

we have given here Alexandria to Syene distance = 500 miles

the sun is 1/50th of the circumference of the sky (about 7°)

as we know that Earth circumference done by astronomer Eratosthenes in 240 B.C

He observe on a particular time of day ( in noon) during the summer solstice

and there was no shadow in Syene in Egypt so This was verified that the sun must be directly on overhead and not at an angle to the surface of the city at that time

so

In Alexandria he measured the position of sun at the same time and found it to be nearly (1/50)th of a complete circle

it would be 7.2 degree (when we do
`(360)/(50)` = 7.2)

so 2 reference points being 2 cities for the sun

all measure circumference = the distance between these two cities × 50

and we have given 500 miles

so

Earth circumference = 500 × 50

Earth circumference is 25000 miles

correct option is 25,000 miles