volume

[tǐ jī]

Terminology of geometry

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This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

Volume, geometry major term 。 When object Occupying space In three-dimensional space, the size of the space occupied is called the volume of the object. Volumetric International System of Units yes cubic metre 。 One-dimensional space Objects (e.g Line ）And 2D space Objects (e.g square ）It's all zero volume.

Chinese name: volume
Foreign name: volume
Column volume formula: V=Sh

Cone volume formula: V=Sh/3
Spherical volume formula: V=4/3πr³
expression: V=m/ρ
Pinyin: tǐ jī

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concept

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When the space occupied by an object is three-dimensional space, the size of the space occupied is called the volume of the object.

Example 1: The volume of a wooden box is 3 cubic meters;

2: When electrolyzing water, two volumes of hydrogen and one volume of hydrogen are released oxygen 。

Historical development

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Figure 1 Zu Chongzhi

China is also the first country in the world to obtain the correct formula for calculating the ball volume Southern Dynasties Mathematician Zu Chongzhi Europe Man was about a thousand years earlier. He also meticulously studied the art of celestial calculation (referring to astronomy and mathematics), Intensive treatment The calendar of the Ming Dynasty was officially issued in 510 after repeated requests from him. He also made a bronze sundial (a kind of measuring device shadows cast by the sun The method of timing) Clepsydra There are many kinds of precision observation instruments, which are adopted by later generations.

(Figure 1 is the first person in the world who calculated the volume of the ball ----- a famous mathematician in ancient China Zu Chongzhi ）

volume The size of the space occupied by the object is called the volume of the object^[1] 。 Volumetric International System of Units yes cubic metre 。 The volume of a solid object is a numerical value used to describe the volume of the object three-dimensional space The space occupied. One-dimensional space Objects (e.g Line ）And 2D space Objects (e.g square ）On three-dimensional Space is zero volume.^[2]

CUoM

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cubic metre 、 Cubic decimeter 、 Cubic centimeter , cubic mm

A cube with an edge length of 1mm and a volume of 1mm

Arris length It's one centimeter cube , volume is 1 cubic centimeter

A cube with edge length of 1 decimeter and volume of 1 cubic decimeter

A cube with a length of 1 meter and a volume of 1 cubic meter

Unit conversion

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1 cubic decimeter=1000 cubic meters centimeter =1000000 cubic millimeters=1 liter=1000 milliliters=0.061 cubic meters inch

1 cubic centimeter=1000 cubic millimeters=1 milliliter=0.000061 cubic inches

1 cubic meter=1000 cubic decimeters=1000000 cubic centimeters=1000000000 cubic millimeters=0.353 cubic feet=1.3079 cubic yards

1 cubic inch=0.016387 cubic decimeter=16.387 cubic centimeter=16387 cubic millimeter

1 cubic foot=28.3 cubic decimeters=28300 cubic centimeters=28300000 cubic millimeters

1 cubic yard=27 cubic feet=0.7646 cubic meters=164.6 cubic decimeters=164600 cubic centimeters=164600000 cubic millimeters

1 cubic foot=31.143 Bushel (UK)=32.143 bushels (US)

1 gallon (US)=0.0037854118 cubic meters=0.8326741845 gallons (UK)

computing method

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Box, cube and cylinder

Volume formula is a formula for calculating volume, that is, a mathematical formula for calculating the volume of various geometric bodies. For example: cylinder 、 prism 、 cone , table body, sphere, ellipsoid, etc.

Volume formula: calculate various forms enclosed by planes and surfaces.

Generally speaking, a geometry is a mathematical formula for the volume of a figure formed by a face, intersection line (where the face intersects with the face), intersection point (where the intersection line intersects or where the surface converges)^[3] 。

The following are the calculation formulas of different graph volumes:

Box ：