Question

The Greek mathematician Eratosthenes (ca. 276-195 BC) measured the circumference of the earthfrom the following observations. He noticed that on a certain day the sun shone directly down a deep wellin Syene (modern Aswan). At the same time in Alexandrea, 500 miles north (on the same meridian), therays of the sun shone at an angle of 7.2° to the zenith. Use this information to find theradius and circumference of the earth.

Answer 1

Answer:

Radius of the Earth is 3978.8 Miles

Circumference of the Earth is 25000 Miles

Step-by-step explanation:

The angle of the sun shone at an angle of 7.2° to the zenith

This means that the angle of the sector of the circle is 7.2° (θ)

S = Length of the sector of the circle = 500 miles

r = radius of earth

Converting 7.2° to radians

$\theta =7.2\frac{\pi}{180}$

$S=r\theta\\\Rightarrow r=\frac{S}{\theta}\\\Rightarrow r=\frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow r=3978.8\ Miles$

∴ Radius of the Earth is 3978.8 Miles

$C=2\pi r\\\Rightarrow C=2\times \pi \frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow C=25000\ Miles$

∴ Circumference of the Earth is 25000 Miles