Kepler's Conjecture postulates that these objects can be packed with a density of approximately 74%. The Banach-Tarski paradox states that a solid one of these objects can be cut into finitely many pieces and re-assembled into two copies of the same size as the original. For a  non-Euclidean geometry occurring on these objects, triangles have angle sum greater than 180 degrees. (*) Archimedes derived the formula for the volume of this figure by noting that it occupied two-thirds of the volume of its circumscribed cylinder. This figure has surface area equal to four pi times the radius squared,
Kepler's Conjecture postulates that these objects can be packed with a density of approximately 74%. The Banach-Tarski paradox states that a solid one of these objects can be cut into finitely many pieces and re-assembled into two copies of the same size as the original. For a  non-Euclidean geometry occurring on these objects, triangles have angle sum greater than 180 degrees. (*) Archimedes derived the formula for the volume of this figure by noting that it occupied two-thirds of the volume of its circumscribed cylinder. This figure has surface area equal to four pi times the radius squared, and volume four-thirds pi times radius cubed. For ten points, name this three-dimensional analogue of a circle, the outer surface of a ball.
Kepler's Conjecture postulates that these objects can be packed with a density of approximately 74%.
{sphere} (accept {ball} before mentioned)