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Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space
As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.
Both formulas can be determined by using Pythagorean theorem. The surface area of a cube is six times the area of a square: [4] =. The volume of a cuboid is the product of its length, width, and height. Because all the edges of a cube are equal in length, it is: [4] =.
The formula for the volume of a pyramid, base area × height 3 , {\displaystyle {\frac {{\text{base area}}\times {\text{height}}}{3}},} had been known to Euclid , but all proofs of it involve some form of limiting process or calculus , notably the method of exhaustion or, in more modern form, Cavalieri's principle .
The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material: = / Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: = Its unit of measurement in the International System of Units (SI) is newton per cubic metre (N/m 3), with ...
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.
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