Solid · Spheres
Sphere
All points at distance r from the centre: the solid ball and its surface.
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Dimensions
Results
volume V
surface area S
Formulas
Archimedes showed the ball is two thirds of the cylinder that just contains it, in volume and in surface. He asked for this on his tombstone.
Checked: the V, S formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a ball: its surface can be stretched onto a sphere without tearing, so its Euler characteristic is 2. More on the lens.