Volume of a prism = cross-section area*length
Volume of a pyramid = 1/3*base area*height
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The biggest impact I think of: Calculus is how people invented the formulas to get the volume and surface area of spheres/cones/pyramids.
that would depend on the shape of the volume. for a box, it would be width * depth * height For a sphere it would be (4 * pi * radius^3) / 3 Pyramids, cones, and other shapes, of course, will have their own formulas.
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democritus calculated the volume of pyramids and cones
if you need to find the volume of the pyramid in rome