What is Volume: Definition and 1000 Discussions

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or 3D shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. 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.
Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.
In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

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  1. A

    How to determine the pressure when you dont have the volume

    Hello! I am having trouble with this problem I found online,it was listed under the "easy" category yet I am somehow not seeing the trick. First I converted the V into m^3 so that V = 0,015 m^3,than I converted the hPa into Pa so p = 101300 Pa and now I used the fact that ##p1V1 = p2V2 ## We...
  2. D

    Volume integral of x^2 + (y-2)^2 +z^2 = 4 where x , y , z > 0

    (a) i sketched a quarter of a sphere centred at x=0 , y=2 , z=0 (b ) ∫ ∫ √ (4-x2 - (y-2)2) dx dy with limits 0 < x < 2 and 0 < y <4 (c ) i converted to spherical polars and took the integrand as 1/r2 . the volume element is r2sinθ drdθd∅ This leads to the triple integral of sinθ with...
  3. B

    How Do You Determine The Number Of Moles In A Volume Of Gas?

    Sadly, I don't even know what I don't know. Could somebody generate a ballpark figure of how many moles of hydrogen you might have in a sphere 2 meters across, 75F and roughly 16 psi? Even with all that information I'm clueless. (I'll now resume twig-fishing for termites...)
  4. M

    Chemistry Adding sugar to water; water level doesn't go back to the original volume

    What are we missing in this experiment? Thanks
  5. yucheng

    Volume of 4-ball by Cavalieri's principle?

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  6. Frabjous

    I Volume of Polyhedra: Smart Systematic Solutions

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  7. D

    Chemistry Volume of a Gas from a thermal decomposition

    Ca(HCO3)2 -> CaCO3 + H2O + CO2 First I evaluate the moles of calcium carbonate (don't mind the units, just to save time) ##\frac {80.0}{40,00+12.01+3*16,00}= 0,799 mol## From the equation, correct me if I am wrong , one mole of CaCO3 is proportional to one mole of CO2, so from this I can...
  8. catlip

    Engineering Should the # of atoms in a unit cell be considered to find the % volume change?

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  9. D

    What to fill a glass bottle with (a liquid that hardens) to lower its volume?

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  10. sandmanvgc

    (Dry) Volume Ideal Gas Law Calculation

    If the question was asking for (dry) volume, how would you do that?
  11. I

    Significant Figures of 225.0 & Molar Volume at STP

    What are the number of significant figures of 225.0? I think it is 4, but the solution says it's 3. Also, is the significant figures of molar volume at STP (22.7 L/mol) considered? Thanks.
  12. E

    I Kirchhoff's law of thermal radiation/Infinitesimal volume

    Is there a form of Kirchhoff's law of thermal radiation that applies to infinitesimal volumes rather than optical surfaces of materials?
  13. E

    B Volume of a solid at absolute zero

    How much does a typical solid shrink when cooled from room temperature to absolute zero. I can't solve this myself because the coefficient of linear thermal expansion varies with temperature
  14. P

    Gas in mercury manometer, finding its normal volume

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  15. S

    3D Volumetric Strain and Volume Change

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  16. H

    A Triangulation and Discrete Volume Spectrum in Covariant LQG

    What is often said in Covariant LQG is that the triangulation is a truncation, and is not what is responsible for the discrete volumes one ends up with in the theory. Rather, what is responsible is the discrete spectra of the volume operator acting on the nodes of a spin network. My confusion...
  17. George Keeling

    I Const Curvature Scalar & 3-Torus: Is It Maximally Symmetric?

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  18. bobbyg

    Relative volume of combusted hydrogen

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  19. J

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  20. AHSAN MUJTABA

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  21. mktsgm

    Medical How is blood volume calculated and measured in the human body?

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  22. P

    Finding Force and Energy from an indentation into a volume

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  23. jaychay

    MHB Find the volume by using shell and disk method

    Can you check it for me please that I have done it right or not ? Thank you in advance.
  24. greg_rack

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  25. jaychay

    MHB Find the volume by using shell and disk method

    Can you check it for me that I done it right or not ? Thank you in advance.
  26. E

    Volume Of Intersection Between Square Pyramid And Sphere

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  27. jaychay

    MHB Find the volume using shell and disk method

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  28. Hamiltonian

    B Volume of paraboloid in a cylinder

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  29. S

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  30. K

    Finding the Volume of an Ideal Gas

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  31. B

    Volume Flow Rate: Open vs Closed Valves

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  32. anuttarasammyak

    Is Bernoulli's Theorem an Expression of Energy Density in Fluids?

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  33. Buzz Bloom

    I Q: Volume of the largest ellipsoid in space which contains no stars?

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  34. Yokoko

    Chemistry Help with mol and volume calculations - Cram's rule

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  35. WMDhamnekar

    MHB Exploring Robert Boyle's Law: Pressure and Volume of CO2

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  36. K

    Velocity, barrel length and bore volume

    Hello. How does a bullet propell inside a bore? What determine its velocity? I read that a bullet in cal .44 propelled by black powder from a 3” barrel is as powerful as a .25 ACP, however with a longer barrel, the velocity increase significant. With a 8” barrel a .44 black powder bullet is as...
  37. Gh778

    B Energy needed to increase a volume

    A recipient (cube) of 1m³ is filled of small spheres, there are for example 1000³ spheres inside the recipient. There are also 1000³ elastics that attract the spheres to the bottom. The elastic are always vertical. One elastic for each sphere. One end of the elastic is fixed on a sphere and the...
  38. J

    MHB Calculate volume of non parallel wedge

    Hi, just wondering how I would calculate the volume of this wedge? see photo attached
  39. notaphysicsmajor79

    Brain function & bipolar: fluid volume & speed of information in tubes

    This is a long post with limited amount of physics in it (but it is a physics question, so hopefully it is allowed). I am a scientist but trained as an ecologist (PhD) and despite my long interest in physics, my knowledge of it remains rather rudimentary. Apologies for that, in advance. I am...
  40. A

    MHB Good day, Exam Integrals: volume and area

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  41. G

    Exploring Balloon Volume in Ocean Descents

    Hey fellow physics enthusiasts, how might the volume of a balloon change as you bring it down deep into the ocean (consider both adiabatic (quick) and equilibrium (slow) descend). Looking for insights what most likely will happen, for simplicity we can start with a thin (##t << R##) elastic...
  42. L

    Magnetic field of a rotating disk with a non-uniform volume charge

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  43. Wrichik Basu

    How Do Android Volume Controls Vary Across Different Devices?

    Summary: If you own an Android phone and are interested in helping me, please navigate to Settings → Sounds. Here, you will find the volume controls (in some phones, you will have an option "Volume" under which you will find all the controls). Please give me the following: a screenshot of the...
  44. Adesh

    I Why volume is conserved but not the surface area?

    A water drop of radius ##10^{-2}## m is broken into 1000 equal droplets. Calculate the gain in surface energy. Surface Tension of water is ##0.075 ~N/m##. So, for the solution of the above problem we need to know how much surface area (combining all 1000 droplets) have increased from the...
  45. Traced

    Find the range of possible dimensions for a volume

    I understand how to get the dimensions that equal 8436m^3. What I don't understand is how to find the range of all possible dimensions. I solved the inequality to get ##6w^{3}-13w^{2}-5w-8436## Using systematic guessing I found the root is x=4, so the factor is x-4. Dividing (x-4) into...
  46. Like Tony Stark

    Determine the heat capacity at a constant volume for a Van der Waals gas

    Hi, what I've done so far is solving equation 2) for ##U##, and replacing what I get in equation 1). Then, ##c_V## is equal to the partial derivative of ##S## with respect to T times T, so I've done that. The derivative is ##CNR/T##, so ##c_V=CNR## but those aren't the correct units for ##c_V##.
  47. karush

    MHB APC.5.2.01 AP Volume by Rotation

    $\displaystyle\pi\int_{0}^{\infty} e^x \ dx = \pi$ Ok I looked at some of the template equations but came up with this.
  48. agnimusayoti

    Volume in the first octant bounded by the coordinate planes and x + 2y + z = 4.

    First, I try to make a sketch and from that I take limit of integration from: 1. ##z_1 = 0## to ##z_2 = 4 - x -2y## 2. ##x_1 = 0## to## x_2 = 4- 2y ## 3. ##y_1 = 0## to ##y_2 = 2## Then, I define infinitesimal volume element in the first octant as ##dV = 1/8 dz dz dy##. Therefore, $$V=1/8...
  49. H

    MHB Volume and surface area of "One World Trade Center"

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  50. agnimusayoti

    How to model a function of a box's volume using Lagrange multiplier methods

    I started to understand how to apply Lagrange multiplier methods. But, for problem like this, I have difficulty to build the function to describe the volume that will be maximized. For the second question, I know from the example (in ML Boas) that ##V=8xyz## becase (x,y,z) is in the 1st octant...
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