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# Spheres

## Volume and surface area of 3D circles.

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Where We Live!

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

Around 220 BCE, a Greek scholar named Eratosthenes managed to calculate the circumference of the Earth with remarkable accuracy, using only his knowledge of shadows, angles, and distance. Unfortunately, his measurements were lost to history, and for 1,500 years people believed that the Earth was flat. Now we know that the Earth is not flat, but also not quite a sphere. What shape is it, and why?

#### Amazing But True

All of the planets are spherical because they rotate, as rotation spreads their mass through centrifugal force. However, since there is more mass in the equatorial plane, it tends to pull mass from the poles. As a result, Earth has the shape of an oblate spheroid, or a flattened sphere.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

This proved to be an embarrassment during the French Revolution: French scientists wanted to create a new system of weights and measurements, basing them on the kilogram and the meter. They defined a meter as 110,000\begin{align*}\frac{1}{10,000}\end{align*} of a quarter of the Earth's circumference, believing the Earth to be a perfect sphere. Unfortunately, because the Earth is not a perfect sphere, the meter had different lengths depending on where you measured it! Today, we use a more accurate system to define our measurements.

Hear one account of Eratosthenes' feat, as told by astronomer Carl Sagan:

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