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There is no universal formula for volume: it depends on the shape. There are formulae for the volumes of some shapes such as cuboids (including cubes), cones, ellipsoids (including spheres), regular polyhedra (including pyramids), prisms (including cylinders). But there are many more irregular shapes for which no formulae exist.
democritus calculated the volume of pyramids and cones
Cones have curved lateral surface, pyramids don't.
The biggest impact I think of: Calculus is how people invented the formulas to get the volume and surface area of spheres/cones/pyramids.
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