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Volume
Volume is a measure of regions in three-dimensional space. 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 volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape ...
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Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ...
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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 , 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 , and is used in the United States and some Latin American and Caribbean countries. There are four gills in a pint, two pints in a quart, and four quarts (''quarter'' gallons) in a gallon, with the imperial gill being divided into five imperial fluid ounces and the US gill being divided into four US fluid ounces: this, and a slight difference in the sizes of the imperial fluid ounce and the US fluid ounce, give different sizes for the imperial gallon and US gallon. The IEEE standard symbol for both the imperial and US gallons is gal, not to be confused with the gal (symbol: Gal), a CGS unit of acceleration. Definitions ...
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Cup (unit)
The 'cup'' is a cooking weights and measures, cooking measure of volume, commonly associated with cooking and serving sizes. In the US customary system, it is equal to . Because actual drinking cups may differ greatly from the size of this unit, standard measuring cups may be used, with a metric cup commonly being rounded up to 240 millilitres (''legal cup''), but 250 ml is also used depending on the measuring scale. United States Customary cup In the United States, the customary cup is half of a Pint#US liquid pint, US liquid pint. Legal cup The cup currently used in the United States for nutrition labelling is defined in United States law as 240 :millilitre, ml. Conversion table to US legal cup The following information is describing that how to measure US legal cup in different ways. Coffee cup A "cup" of coffee in the US is usually 4 fluid ounces (118 ml), brewed using 5 fluid ounces (148 ml) of water. Coffee carafes used with drip coffee makers, e.g. Black an ...
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Fluid Ounce
A fluid ounce (abbreviated fl oz, fl. oz. or oz. fl., old forms ℥, fl ℥, f℥, ƒ ℥) is a unit of volume (also called ''capacity'') typically used for measuring liquids. The British Imperial, the United States customary, and the United States food labeling fluid ounce are the three that are still in common use, although various definitions have been used throughout history. An imperial fluid ounce is of an imperial pint, of an imperial gallon, or exactly 28.4130625 mL. A US customary fluid ounce is of a US liquid pint, of a US gallon, or exactly 29.5735295625 mL, making it about 4.084% larger than the imperial fluid ounce. A US food labeling fluid ounce is exactly 30 mL. Comparison to the ounce The ''fluid'' ounce is distinct from the (international avoirdupois) ounce as a unit of weight or mass, although it is sometimes referred to simply as an "ounce" where context makes the meaning clear (e.g., "ounces in a bottle"). A volume of pure water me ...
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Millilitre
The litre ( Commonwealth spelling) or liter ( American spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A cubic decimetre (or litre) occupies a volume of (see figure) and is thus equal to one-thousandth of a cubic metre. The original French metric system used the litre as a base unit. The word ''litre'' is derived from an older French unit, the '' litron'', whose name came from Byzantine Greek—where it was a unit of weight, not volume—via Late Medieval Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, despite it not being an SI unit. The SI unit of volume is the cubic metre (m3). The spelling used by the International Bureau of Weights and Measures is "litre",
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Litre
The litre ( Commonwealth spelling) or liter ( American spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A cubic decimetre (or litre) occupies a volume of (see figure) and is thus equal to one-thousandth of a cubic metre. The original French metric system used the litre as a base unit. The word ''litre'' is derived from an older French unit, the '' litron'', whose name came from Byzantine Greek—where it was a unit of weight, not volume—via Late Medieval Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, despite it not being an SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of unit ...
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United States Customary Units
United States customary units form a system of measurement units commonly used in the United States and most U.S. territories since being standardized and adopted in 1832. The United States customary system developed from English units that were in use in the British Empire before the U.S. became an independent country. The United Kingdom's system of measures evolved by 1824 to create the imperial system (with imperial units), which was officially adopted in 1826, changing the definitions of some of its units. Consequently, while many U.S. units are essentially similar to their imperial counterparts, there are noticeable differences between the systems. The majority of U.S. customary units were redefined in terms of the meter and kilogram with the Mendenhall Order of 1893 and, in practice, for many years before. T.C. Mendenhall, Superintendent of Standard Weights and MeasuresOrder of April 5, 1893, published as Appendix 6 to the Report for 1893 of the United States C ...
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Imperial Units
The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed through a series of Weights and Measures Acts and amendments. The imperial system developed from earlier English units as did the Comparison of the imperial and US customary measurement systems, related but differing system of United States customary units, customary units of the United States. The imperial units replaced the Winchester measure, Winchester Standards, which were in effect from 1588 to 1825. The system came into official use across the British Empire in 1826. By the late 20th century, most nations of the former empire had metrication, officially adopted the metric system as their main system of measurement, but imperial units are still used alongside metric units in the United Kingdom and in some other parts of the former empi ...
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Teaspoon
A teaspoon (tsp.) is a small spoon that can be used to stir a cup of tea or coffee, or as a tool for measuring volume. The size of teaspoons ranges from about . For dosing of medicine and, in places where metric units are used, for cooking purposes, a teaspoonful is defined as , and standard measuring spoons are used. Cutlery A teaspoon is a small spoon suitable for stirring and sipping the contents of a cup of tea or coffee, or adding a portion of loose sugar to it. These spoons have heads more or less oval in shape. Teaspoons are a common part of a place setting. Teaspoons with longer handles, such as iced tea spoons, are commonly used also for ice cream desserts or floats. Similar spoons include the tablespoon and the dessert spoon, the latter intermediate in size between a teaspoon and a tablespoon, used in eating dessert and sometimes soup or cereals. Much less common is the coffee spoon, which is a smaller version of the teaspoon, intended for use with the small ...
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Litre
The litre ( Commonwealth spelling) or liter ( American spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A cubic decimetre (or litre) occupies a volume of (see figure) and is thus equal to one-thousandth of a cubic metre. The original French metric system used the litre as a base unit. The word ''litre'' is derived from an older French unit, the '' litron'', whose name came from Byzantine Greek—where it was a unit of weight, not volume—via Late Medieval Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, despite it not being an SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of unit ...
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Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to Ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, ...
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Liquid
Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are classified as condensed matter. Meanwhile, since both liquids and gases can flow, they are categorized as fluids. A liquid is composed of atoms or molecules held together by intermolecular bonds of intermediate strength. These forces allow the particles to move around one another while remaining closely packed. In contrast, solids have particles that are tightly bound by strong intermolecular forces, limiting their movement to small vibrations in fixed positions. Gases, on the other hand, consist of widely spaced, freely moving particles with only weak intermolecular forces. As temperature increases, the molecules in a liquid vibrate more intensely, causi ...
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