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The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
The volume of a prism is the product of the area of the base by the height, i.e. the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance). The volume is therefore: =, where B is the base area and h is the height.
The volume is found by taking the area of the base, with a side length of and apothem , and multiplying it by the height , giving the formula: [1] = This formula also ...
In the case of a triangular prism, its base is a triangle, so its volume can be calculated by multiplying the area of a triangle and the length of the prism: , where b is the length of one side of the triangle, h is the length of an altitude drawn to that side, and l is the distance between the triangular faces. [9]
A tidal prism is the volume of water in an estuary or inlet between mean high tide and mean low tide, [1] or the volume of water leaving an estuary at ebb tide. [2]The inter-tidal prism volume can be expressed by the relationship: P=H A, where H is the average tidal range and A is the average surface area of the basin. [3]