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Volume is a measure of regions in three-dimensional space. [1] It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume
The definitions and results in this section are taken from the 1913 text Plane and Solid Geometry by George A. Wentworth and David Eugene Smith (Wentworth & Smith 1913).. A cylindrical surface is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line.
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
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids , prisms (and other polyhedrons ), cubes , cylinders , cones (and truncated cones ).
The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n -ball of radius R is R n V n , {\displaystyle R^{n}V_{n},} where V n {\displaystyle V_{n}} is the volume of the unit n -ball , the n -ball of radius 1 .
The tun is approximately the volume of a cylinder with both diameter and height of 42 inches, as the gallon was originally a cylinder with diameter of 7 inches and height of 6. [ nb 3 ] The Queen Anne wine gallon of 231 cubic inches was adopted in 1707, and still serves as the definition of the US gallon.
The gallon is a unit of volume in British imperial units and United States customary units.. The imperial gallon (imp gal) is defined as 4.546 09 litres, and is or was used in the United Kingdom and its former colonies, including Ireland, Canada, Australia, New Zealand, India, South Africa, Malaysia and some Caribbean countries, while the US gallon (US gal) is defined as 231 cubic inches (3. ...
Within the cylinder is the cone whose apex is at the center of one base of the cylinder and whose base is the other base of the cylinder. By the Pythagorean theorem , the plane located y {\displaystyle y} units above the "equator" intersects the sphere in a circle of radius r 2 − y 2 {\textstyle {\sqrt {r^{2}-y^{2}}}} and area π ( r 2 − y ...