# Archimedes knew the volume of a sphere

. . . now he had to prove it!

Archimedes built a sphere-like shape from cones
and frustrums (truncated cones)

He drew two shapes around the sphere's center -

one outside the sphere (circumscribed) so its volume was greater than the
sphere's, and
one inside the sphere (inscribed) so its volume was less than the sphere's.

## Here is a bad example, an
inscribed shape made of 2 cones and just 2 frustrums

The more frustrums the shape has, the more
it looks like a sphere.

## This argument allowed
Archimedes to rigorously determine

both the volume and surface area of a sphere!

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