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3. Testimonials - don't know anybody that has bought a Volume? Wrong! If the Volume is good the internet will let you know. Use the Internet as a friend and get testimonials before you buy.
4. Questions - Got a question about Volume then search the Forums, FAQ's, Blogs etc. Don't be afraid to ask .....
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6. Returns - still worried that even after all of the above your Volume wont be what you want? Check out the returns policy. There is so much competition now that someone, somewhere is bound to offer the terms that you are comfortable with.
7. Feedback - happy with your Volume then let people know, after all you are depending on others people input in your buying decision, so why not give a little back.
8. Security - check for the yellow padlock on the Volume site before you buy, and the s after http:/ /i.e. https:// = a secure site
9. Contact - got a question about Volume, or want to leave a comment then check out the sites contact page. Reputable companies have them and respond.
10. Payment - ready to pay for your Volume, then use your credit card or PayPal! Be aware of companies that don't accept them, there may be genuine reasons but given the huge amount of choice you have when buying online there is no reason at all not to buy via credit card or PayPal.
The
volume of a solid object is the three-
dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as
line (mathematics)) and two-dimensional shapes (such as square (geometry)s) are assigned zero volume in the three-dimensional space.
Volumes of straight-edged and circular shapes are calculated using arithmetic formulae. Volumes of other curved shapes are calculated using integral calculus, by approximating the given body with a large amount of small
cube (geometry) or concentric
cylinder (geometry) shells, and adding the individual volumes of those shapes. The volume of irregularly shaped objects can be determined by Displacement (fluid). If an irregularly shaped object floats on water, you will need a heavier object like a rock or metal and attach it on you floating object. This should cause the object to sink. Then, get the volume of the object. Subtract the volume of the attached heavy object and the original findings.
The generalization of volume to arbitrarily many dimensions is called
content. In differential geometry, volume is expressed by means of the volume form.
Volume and Capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in
litres or its derived units), and volume being how much space an object displaces (commonly measured in
cubic metres or its derived units).
Volume and capacity are also distinguished in a capacity management setting, where capacity is defined as volume over a specified time period.
Volume is a fundamental parameter in thermodynamics and it is conjugate variables (thermodynamics) to pressure.
Volume formulae
{| class=prettytable|-! colspan = 3 | Common equations for volume:]:|s^3 = s \cdot s \cdot s|
s = length of a side|-|A rectangular
Prism (geometry):|l \cdot w \cdot h|l =
length, w =
width, h =
height|-|A cylinder (geometry) (circular prism):|\pi r^2 \cdot h|
r = radius of circular face,
h = height|-|Any prism that has a constant cross sectional area along the height**:|A \cdot h|
A = area of the base,
h = height|-|A
sphere:] of the Surface Area of a
sphere:|\frac{4}{3} \pi abc|a, b, c = semi-axes of ellipsoid|-|A [Pyramid (geometry):|\frac{1}{3} lwh|l =
length, w =
width, h =
height|-|A Cone (geometry) (circular-based pyramid):|\frac{1}{3} \pi r^2 h|
r = radius of circle at base,
h = distance from base to tip] required)|\int A(h) \,dh|
h = any dimension of the figure,
A(
h) = area of the cross-sections perpendicular to
h described as a function of the position along
hthis will work for any figure if its cross-sectional area can be determined from h (no matter if the prism is slanted or the cross-sections change shape).
|}
(The units of volume depend on the units of length - if the lengths are in metres, the volume will be in cubic
metres, etc)
The volume of a
parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix.
The volume of any tetrahedron, given its vertices
a,
b,
c and
d, is (1/6)·](
a−
b,
b−
c,
c−
d)|, or any other combination of pairs of vertices that form a simply connected
graph theory.
Volume measures: USA
U.S. customary units of volume:
- U.S. fluid ounce, about 29.6 mL
- U.S. liquid pint = 16 fluid ounces, or about 473 mL
- U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries)
- U.S. liquid quart = 32 fluid ounces, or about 946 mL
- U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L
- U.S. liquid gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L
- U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L
- U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L
The
acre foot is often used in measuring the volume of water in a
reservoir (water) or an
aquifer. It is the volume of water that would cover an
area of one acre to a depth of one
foot (unit of length). It is equivalent to 43,560 cubic feet or exactly 1233.481 837 547 52 m³.
- cubic inch = 16.387064 cm³
- cubic foot = 1,728 in³ ≈ 28.317 dm³
- cubic yard = 27 ft³ ≈ 0.7646 m³
- cubic mile = 5,451,776,000 yd³ = 3,379,200 acre-feet ≈ 4.168 km³
Volume measures: UK
The UK is undergoing
metrication and is increasingly using the
International System of Units units of volume, i.e. cubic meter and litre. However, some former units of volume are still in varying degrees of usage:
Imperial units of volume:
- UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions)
- UK pint = 20 fluid ounces, or about 568 mL
- UK quart = 40 ounces or two pints1.137 L
- UK gallon = 4 quarts, or exactly 4.546 09 L
The quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol and diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer and cider (bottled and canned beer is mainly sold in SI units) and for milk (this too is increasingly being sold in SI units, mainly Liters).
Volume measures: cooking
Traditional cooking measures for volume also include:
- teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
- teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL)
- teaspoon = 5 mL (metric)
- tablespoon = ½ U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
- tablespoon = ½ Imperial fluid ounce or 3 teaspoons (about 14.21 mL)
- tablespoon = 15 mL or 3 teaspoons (metric)
- tablespoon = 5 fluidrams (about 17.76 mL) (British)
- Cup (unit) = 8 U.S. fluid ounces or ½ U.S. liquid pint (about 237 mL)
- cup = 8 Imperial fluid ounces or ½ fluid pint (about 227 mL)
- cup = 250 mL (metric)
Relationship to density
The volume of an object is equality (mathematics) to its
mass division (mathematics) by its average density. This is a rearrangement of the calculation of density as mass per unit volume.
The term
specific volume is used for volume divided by mass. This is the
Reciprocal (mathematics) of the mass density, expressed in units such as cubic meters per kilogram (m³·kg-1).
See also
- Area
- Conversion of units#Volume
- Density
- Orders of magnitude (volume)
- Mass
- Ton (volume)
External links
- FORTRAN code for finding volumes of various shapes
The
volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as
line (mathematics)) and two-dimensional shapes (such as square (geometry)s) are assigned zero volume in the three-dimensional space.
Volumes of straight-edged and circular shapes are calculated using arithmetic formulae. Volumes of other curved shapes are calculated using
integral calculus, by approximating the given body with a large amount of small cube (geometry) or concentric cylinder (geometry) shells, and adding the individual volumes of those shapes. The volume of irregularly shaped objects can be determined by Displacement (fluid). If an irregularly shaped object floats on water, you will need a heavier object like a rock or metal and attach it on you floating object. This should cause the object to sink. Then, get the volume of the object. Subtract the volume of the attached heavy object and the original findings.
The generalization of volume to arbitrarily many dimensions is called
content. In
differential geometry, volume is expressed by means of the
volume form.
Volume and Capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units).
Volume and capacity are also distinguished in a capacity management setting, where capacity is defined as volume over a specified time period.
Volume is a fundamental parameter in thermodynamics and it is conjugate variables (thermodynamics) to
pressure.
Volume formulae
{| class=prettytable|-! colspan = 3 | Common equations for volume:]:|s^3 = s \cdot s \cdot s|
s = length of a side|-|A rectangular
Prism (geometry):|l \cdot w \cdot h|l =
length, w =
width, h =
height|-|A
cylinder (geometry) (circular prism):|\pi r^2 \cdot h|
r = radius of circular face,
h = height|-|Any prism that has a constant cross sectional area along the height**:|A \cdot h|
A = area of the base,
h = height|-|A sphere:] of the
Surface Area of a
sphere:|\frac{4}{3} \pi abc|a, b, c = semi-axes of ellipsoid|-|A [Pyramid (geometry):|\frac{1}{3} lwh|l =
length, w =
width, h =
height|-|A
Cone (geometry) (circular-based pyramid):|\frac{1}{3} \pi r^2 h|
r = radius of
circle at base,
h = distance from base to tip] required)|\int A(h) \,dh|
h = any dimension of the figure,
A(
h) = area of the cross-sections perpendicular to
h described as a function of the position along
hthis will work for any figure if its cross-sectional area can be determined from h (no matter if the prism is slanted or the cross-sections change shape).
|}
(The units of volume depend on the units of length - if the lengths are in metres, the volume will be in cubic
metres, etc)
The volume of a parallelepiped is the absolute value of the
scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix.
The volume of any
tetrahedron, given its vertices
a,
b,
c and
d, is (1/6)·](
a−
b,
b−
c,
c−
d)|, or any other combination of pairs of vertices that form a simply connected
graph theory.
Volume measures: USA
U.S. customary units of volume:
- U.S. fluid ounce, about 29.6 mL
- U.S. liquid pint = 16 fluid ounces, or about 473 mL
- U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries)
- U.S. liquid quart = 32 fluid ounces, or about 946 mL
- U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L
- U.S. liquid gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L
- U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L
- U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L
The
acre foot is often used in measuring the volume of water in a reservoir (water) or an aquifer. It is the volume of water that would cover an
area of one
acre to a depth of one
foot (unit of length). It is equivalent to 43,560 cubic feet or exactly 1233.481 837 547 52 m³.
- cubic inch = 16.387064 cm³
- cubic foot = 1,728 in³ ≈ 28.317 dm³
- cubic yard = 27 ft³ ≈ 0.7646 m³
- cubic mile = 5,451,776,000 yd³ = 3,379,200 acre-feet ≈ 4.168 km³
Volume measures: UK
The UK is undergoing
metrication and is increasingly using the
International System of Units units of volume, i.e. cubic meter and litre. However, some former units of volume are still in varying degrees of usage:
Imperial units of volume:
- UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions)
- UK pint = 20 fluid ounces, or about 568 mL
- UK quart = 40 ounces or two pints1.137 L
- UK gallon = 4 quarts, or exactly 4.546 09 L
The quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol and diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer and cider (bottled and canned beer is mainly sold in SI units) and for milk (this too is increasingly being sold in SI units, mainly Liters).
Volume measures: cooking
Traditional cooking measures for volume also include:
- teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
- teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL)
- teaspoon = 5 mL (metric)
- tablespoon = ½ U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
- tablespoon = ½ Imperial fluid ounce or 3 teaspoons (about 14.21 mL)
- tablespoon = 15 mL or 3 teaspoons (metric)
- tablespoon = 5 fluidrams (about 17.76 mL) (British)
- Cup (unit) = 8 U.S. fluid ounces or ½ U.S. liquid pint (about 237 mL)
- cup = 8 Imperial fluid ounces or ½ fluid pint (about 227 mL)
- cup = 250 mL (metric)
Relationship to density
The volume of an object is
equality (mathematics) to its
mass division (mathematics) by its
average density. This is a rearrangement of the calculation of density as mass per unit volume.
The term
specific volume is used for volume divided by mass. This is the Reciprocal (mathematics) of the mass density, expressed in units such as cubic meters per kilogram (m³·kg-1).
See also
External links
- FORTRAN code for finding volumes of various shapes
Volume - Partners in Marketing
Volume - Partners in Marketing
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Parcel Volume Calculator | Parcel2Go.com
Use our parcel volume calculator to calculate either UK or international chargable weight.
