1. Volume can be simply defined as the size or extent of something. Term widely used in everyday life as well as in various areas such as geometry, physics and bibliography. Examples: a) ‘I received a large volume of tasks for this week’; b) ‘the flow of the river is going down a lot this winter’.
2. In reference to sound, volume refers to its level of intensity, at the high and low ends, which, depending on the case, allows its manipulation. Example: ‘I turned up the volume on the TV so everyone could hear the news’.
3. Bibliology. In a work or periodical, the volume is equivalent to an individual printed part that is related to the publication as a constituent part thereof, either as a continuation (eg, ‘a 10-volume work’) or as a function of the publication. in a chronological order (eg, ‘volume 01 of the year 2000’).
4. physics/geometry. Extension of the three dimensions -height+width+length- of a body, that is, the volume is the space occupied by an element quantified in cubic meters (m³).
Etymology: by latin volumeas a ‘roll’, linked to the handling of papyri, manuscripts, associated with the verb I will be backfrom ‘enrollar’, and which refers to the word ‘return’.
Grammatical category: masculine noun
in syllables: volume.
Volume (in Physics)
Evelyn Maitee Marin
Industrial Engineer, MSc in Physics, and EdD
Volume is a scalar physical quantity that expresses the three-dimensional space occupied by a body. It is a derived quantity, formed by the dimension of length raised to the cube [L]3, so the units of volume are:
• In the International System of Units: cubic meters (m3)
• In the English system: cubic feet (ft3)
• In the CGS system: cubic centimeters (cm3)
In general, any length cubed is used to express a volume, for example, inches cubed (in3), cubic yards (yd3), cubic millimeters (mm3), cubic kilometers (km3), etc.; whether it is a solid, liquid or gaseous substance.
Regarding the physical properties of substances, these can be intensive or extensive, and in regards to volume, it is an extensive amount, that is, its value depends on the amount of matter.
On the other hand, from the practical point of view, the volume is considered an indirect measurement, since its value is determined from equations that involve two or more direct measurements, which are determined with instruments to measure length, for example, to calculate the volume of a cylinder with a circular base, there is no instrument that directly serves to measure this volume, instead, its height and diameter are measured and these values are substituted in the formula for calculating the volume of a cylinder .
Volume of geometric figures
All matter occupies a volume in space, however, there are no formulas available to calculate the infinite volumes that exist. For common geometric solids, formulas are available that make it possible to easily determine this parameter in said figures. For example, for figures of constant cross section, say cubes, parallelepipeds, cylinders, or prisms of regular section; The volume is found by multiplying the area of its base by the height.
The following table shows some volume formulas for common geometric figures:
Cube
\(V={{a}^{3}}\)
Parallelepiped
\(V= a \cdot b \cdot c\)
circular base cylinder
\(V=\pi \cdot {{r}^{2}} \cdot h\)
Sphere
\(V=\frac{4}{3} \cdot \pi \cdot {{r}^{3}}\)
square base pyramid
\(V=\frac{1}{3} \cdot {{a}^{2}} \cdot h\)
Pussy
\(V=\frac{1}{3} \cdot \pi \cdot {{r}^{2}} \cdot h\)
• When the body is a solid of irregular shape, other methods or techniques are used to determine its volume, for example, immersing the body in a fluid of known density (water) contained in a scaled and calibrated container, so that the volume of displaced fluid equals the volume of the body.
• Likewise, in some applications in which the equations of the surfaces that delimit the contour of the body are known, integrals can be used to calculate the volume of the solid.
• In the case of composite figures, such as a hollow spherical shell or a pipe with a given wall thickness, the volume of the solid can be calculated from the difference in the volume of the external figure, minus the volume occupied by the hollow region. .
Relationship between volume and capacity
Capacity refers to the empty space of some object that can contain a volume, therefore there is a relationship between capacity and volume. Thus, it is possible to demonstrate experimentally that if a calibrated container with a capacity of 1 liter is available and it is filled with the water that was contained in a cube whose edges measure 10 cm, it can be determined that 1 liter of water is equivalent to 1000 cm3 of this substance (10 cm x 10 cm x 10 cm = 1000 cm3).
Volume Calculation Example
You want to determine the volume in m3 of a cylinder whose dimensions are shown in the image:
In this case, the first step requires performing a unit conversion in order to unify the dimensions. It is known that 1 foot = 0.3048 m.
\(1.2~ft\times \frac{0.3048~m}{1~ft}=0.3658~m\)
Taking the units in the same system, we proceed to determine the volume of the cylinder:
\(V=\pi \cdot {{r}^{2}} \cdot h=\pi \cdot {{\left( 0.3658 \right)}^{2}} \cdot \left( 7.3 \right)\)
The volume of the cylinder is:
V = 3.07 m3
volume applications
In Physics, Chemistry and other areas, it is not only important to know the volume of a body itself; In addition, this value is usually very useful to develop other calculations or analyses, for example, the volume is used to:
• Express the concentration of a substance
• Calculate the density of a body or material
• Determine the buoyant force exerted by a liquid
• Find the force applied by a fluid on a submerged surface.
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