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An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
Consider the linear subspace of the n-dimensional Euclidean space R n that is spanned by a collection of linearly independent vectors , …,. To find the volume element of the subspace, it is useful to know the fact from linear algebra that the volume of the parallelepiped spanned by the is the square root of the determinant of the Gramian matrix of the : (), = ….
The wine gallon, which some sources relate to the volume occupied by eight medieval merchant pounds of wine, was at one time defined as the volume of a cylinder 6 inches deep and 7 inches in diameter, i.e. 6 in × (3 + 1 / 2 in) 2 × π ≈ 230.907 06 cubic inches.
Oil conversion factor from m³ to bbl (or stb) is 6.28981100 Gas conversion factor from standard m³ to scf is 35.314666721 Note that the m³ gas conversion factor takes into account a difference in the standard temperature base for measurement of gas volumes in metric and imperial units.
The Winchester bushel is the volume of a cylinder 18.5 in (470 mm) in diameter and 8 in (200 mm) high, which gives an irrational number of approximately 2150.4202 cubic inches. [4] The modern American or US bushel is a variant of this, rounded to exactly 2150.42 cubic inches, less than one part per ten million less. [ 5 ]
An imperial fluid ounce is 1 ⁄ 20 of an imperial pint, 1 ⁄ 160 of an imperial gallon or exactly 28.4130625 mL. A US customary fluid ounce is 1 ⁄ 16 of a US liquid pint and 1 ⁄ 128 of a US liquid gallon or exactly 29.5735295625 mL, making it about 4.08% larger than the imperial fluid ounce. A US food labeling fluid ounce is exactly 30 mL.
The formula for the volume of a frustum of a paraboloid [23] [24] is: V = (π h/2)(r 1 2 + r 2 2), where h = height of the frustum, r 1 is the radius of the base of the frustum, and r 2 is the radius of the top of the frustum. This allows us to use a paraboloid frustum where that form appears more appropriate than a cone.
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 ...