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. MevsEinstein

    What has a shape but no volume?

    I was reading a Chemistry book when I read about the three states of matter. Everyone knows what they are, but I didn't know the simplest way to describe each of the three until I read this book. It said that a solid has a shape and a volume, a liquid has no shape but has a volume, and a gas has...
  2. Tertius

    I Computing Volume in General Relativity: Use of Tensor & Friedmann Eqns

    When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...
  3. PainterGuy

    B Extrapolation of relationship of temperature and volume for gas

    Hi, Originally, the absolute temperature was thought to be around -273 Celsius around 1750 and it was the result extrapolation of of ideal gas law as shown below. I find it hard to phrase my question. But the question is how come they were so confident that the relationship between the volume...
  4. F

    Hot air balloon mass including increase in mass with balloon volume

    Hi guys, M can then be split up into 2 components: the mass of the payload which is known, and the mass of the wing. The wing material has a known thickness and density meaning its mass is given by: surface area of wing* mass per m^2 (mass m^2 is used as density and thickness are known so an...
  5. S

    Volume of solid having triangle base and semicircle slice

    First, I tried to find the equation of line passing through (2, 0) and (0, 3) and I got ##y=3-\frac{3}{2}x## Then I set up equation for the area of one slice, ##A(x)## $$A(x)=\frac{1}{2} \pi r^2$$ $$=\frac{1}{2} \pi \left( \frac{1}{2}y\right)^2$$ $$=\frac{1}{2} \pi...
  6. chwala

    Find the volume of the parallelepiped

    Am refreshing on this; see attached below ok we can also use the form ##[i×j=k, k×i=j , j×k=i]## right? to give us say, ##w⋅(u ×v)=v⋅(w ×u)## in realizing same solution.
  7. Mr_Allod

    Probability of finding a pion in a small volume of pionic hydrogen

    Hello, I am trying to figure out the right way to approach this. First of all, other than the different Bohr radius value, does the change to a negative pion make any other difference to calculating the probability? Also what would be the correct way to apply the "small volume"? What I'm...
  8. chwala

    Find the volume of the given prism

    Find the question below; This is a textbook question and i noted that their solution of, $$A=\left[\dfrac{1}{2}×3×4×6\right]cm^3$$ is not correct in my opinion as the base is not a right angle. The base can be analysed as a rhombus and the exercise therefore is to find the related angles and...
  9. chwala

    Find the greatest and least values of Volume of cylinder

    $$V=πr^2h$$ $$V=πr^2(6-r)$$ $$\frac {dV}{dr}=12πr-3πr^2$$ For max/min value, $$\frac {dV}{dr}=0$$ $$12πr-3πr^2=0$$ $$3πr(4-r)=0$$ ##r=0## or ##r=4## $$⇒V_{max}= 32π$$ $$⇒V_{min}= 0$$, I do not think there is another way of doing...
  10. I

    Biology Volume of substrate affecting enzyme activity

    I know that as the concentration of substrate increases, the enzyme activity increases because there are more substrate molecules to react on (but at an increasingly slower rate). Would the same reasoning work with volume? Thanks!
  11. PeroK

    I Volume of Solid of Revolution (About the line y = x)

    I found this problem, which I thought was interesting and somewhat original: Calculate the volume of the solid of revolution of the area between the line ##y = x## and the parabola ##y = x^2## from ##x = 0## to ##x = 1## when rotated about the axis ##y = x##.
  12. Ophi-Siren-Kit

    Speed/Velocity and Volume Flow Rate of Viscous Fluids

    In my first attempt, I started off converting the radii of all three sections from centimeters (10, 8, 6) to meters (0.10 , 0.08 , 0.06), then used the VFR=Av formula to find the speed/velocity of section one. VFR== 0.063 m^3/s A== pi*r^2=pi*(10cm)^2=pi*(0.10)^2=pi*0.01 == 0.031415927 VFR/A=v...
  13. barryj

    Chemistry Calculating the Volume of a 40% Solution

    Since the density is 1320 g/L then for every L of solution there is 320 grams of solute. 320 is 35% of 900 hence the statement it is is a (about) a 40% solution So the volume that would have 12.5 grams would be 12.5/320 L = .039 L = 39 mL
  14. CynicusRex

    Chemistry Calculating the mass percent from a given volume % and density

    [I've solved b, but can't figure out a for the life of me. I have a couple of attempts, but it's just nonsense, it's like I've short circuited.]
  15. A

    Audio/Video How Can I Create a Touch Sensitive Volume Knob for My Audio Card?

    Hi, I am trying to think how to make a DYI volume knob to control variable actions on my audio card. But I don’t want one with buttons to toggle the actions.. instead I want to make one with a touch sensitive lcd screen and make the scroll knob (a físicas one) around the screen bc I want to use...
  16. es4

    Calculation of pressure & volume both isothermally & adiabatically

    Hi, here is my attempt... Feel free to correct me if I am doing it wrong. v1 = .8 m3 p1 = 250 or 250000 n/m2 p2 = 7000 or 7000000 n/m2 Cp = 1010 Cv = 7321. isothermally p1v1 = p2v2 [Boyle equality law (isothermal process)] 250 000 * .8 = 7000000 * v2 7000000 * v2 = 250 000 * .8...
  17. Philip Koeck

    A Volume constraint in micro-canonical derivation of statistical physics

    Another question about the use of the micro-canonical ensemble in deriving distributions. On the Wikipedia-page the authors mention that the total volume of the system has to be constant. See...
  18. V

    Volume density vs Surface density of charge distribution

    This doubt is confusing to me. I know it's something to do with conductors and insulators, but cannot explain. Conductors have mobile/free electrons unlike insulators. Having free electrons doesn't seem to explain this difference of charge distributions.
  19. mncyapntsi

    Uncertainty, volume, and measurement

    I have done this question and gotten: Vmin = 4pi/3(19.18)^3=29555.2 V = 4pi/3(19.31)^3=30160.3 Vmax = 4pi/3(19.44)^3=30773.5 Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong... Could someone please help me find out where I went wrong, or tell me if I went the wrong...
  20. B

    How do I calculate variance for volume, 𝑉 (i.e, ⟨Δ𝑉2⟩=⟨𝑉2⟩−⟨𝑉⟩2)?

    This is not actually a homework problem. I'm old but having trouble with something that's probably at student level because it's so long since I learned this stuff. I would be grateful if someone would please take pity on me and help me out! I am trying to calculate something that includes...
  21. M

    MHB Calculate the volume of the set M

    Hey! :giggle: We have the set $M=\{(x,y,z)\in \mathbb{R}^3 : x^2+y^2-z^2\leq 1, \ 0 \leq z\leq 3\}$. Draw $M$ and calculate the volume of $M$. I have done the following : \begin{equation*}\int_M\, dV=\int\int\int\, dx\, dy\, dy\end{equation*} Which are the boundaries of the integrals? Do we...
  22. vibha_ganji

    B Definition of Stellar Parallax from Alonso and Finn Volume 1

    Hi! I read this definition of Stellar Parallax "It is expressed quantitatively by one-half the angle subtended by the Earth's diameter E1E2 perpendicular to the line joining the star and the sun (see Fig. 2-10)." (Source Alonso and Finn: Volume 1). But, I was unable to understand how they...
  23. S

    Stock trading volume statistics

    Has the advent of computer trading greatly increased the size of statistics for trading volume? - or do those statistics (for individual stocks) somehow omit the flash trades done by computers? In the pre-computer days, there were people who had theories of stock trading based on both the...
  24. Charles_Xu

    I The definition of volume inside black hole?

    What is the definition of volume inside a black hole? we know the grr element of Schwarzschild metric is negative inside event horizon, so how to define a volume inside event horizon? if there is no definition of volume, is there the definition of density?
  25. A

    MHB Calculate Volume & Surface Area of a Cylinder Without Lid

    how to find volume and surface area of this without using the upper lid
  26. vibha_ganji

    Alonso and Finn Volume 1 Chapter 4 -- A sphere is held against a wall by an inclined plane

    I’m pretty sure that the force on the sphere by the wall and plane has to equal mg so the sum of the normal force is steered by the wall and plane has to equal mg. I’m not sure where to go after this. Is mg the answer or is there something I’m missing?Here is Fig: 4-31:
  27. W

    Volume of solid region double integral

    I sketched this out. With the z=0 and y=0 boundaries, we are looking at ##z \geq 0## and ##y \geq 0## I believe ##0 \leq x \leq 5## because of the boundary of ##y=\sqrt{25-x^2}##. This is my region ##\int_0^5 \int_0^\sqrt{25-x^2} x \, dydx ## ## =\int_0^5 xy \vert_{0}^{\sqrt{25-x^2}} \, dx##...
  28. Istiak

    Calculate the volume change with gas temperature for this piston in a cylinder

    Solution attempt : Option : I am sure that my work is wrong. But, I must add solution attempt in PF that's why I just added that. How can I solve the problem?
  29. sophiecentaur

    Measuring your body volume without getting wet

    Air displacement plethysmography I saw a tv programme many years ago which shows this method of measuring the volume of a patient's body. Air displacement plethysmography was a procedure that I saw being used and, tbh, I never asked myself how it works, until now. It's smart, imo. You put...
  30. N

    I Volume of water consumed by vacuum

    I'm trying to do the math for a backyard thermodynamic pump experiment, and getting stuck. Suppose an empty 3.79 liter container was airlocked by a vertical 25 cm long empty tube whose end sits at the top of an unlimited supply of water in a basin. The tube protrudes through the container such...
  31. Z

    DeltaG and DeltaA calculation for heating a gas at constant volume

    Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A)...
  32. Limebat

    Atmosphere and volume - vacuum cannon limitations

    https://physics.csuchico.edu/~eayars/publications/AJP00961.pdf http://www.phys.utk.edu/demoroom/MECH/The%20Vacuum%20Canon.pdfSo I get the outside atmosphere is what provides air density and such in the pdf above^. However, why is it that most cannon demonstrations use just the air from the...
  33. S

    Volume of the smaller part of a sliced cylinder

    I imagine the shape will be like this: and I need to find the volume of the shaded part. I am planning to use: ##V=\int A(y) dy## I tried to take the cross-sectional area A(y) to be triangle: and the base of the cylinder to be: So it means that the base of the triangle will fulfill the...
  34. M

    MHB How do I calculate the amount from the volume?

    The gold pavilion in the city of Kyoto is covered with gold leaf. Gold leaf has a thickness of 100 nm (nanometres) and is made from gold bars. A gold bar has a volume of 0.65 dm^3. How many square metres can the gold leaf from a gold bar cover?
  35. G

    I How do I calculate density given height and volume?

    I’m trying to calculate how many Joules are stored in the Hyperion tree, the worlds tallest (115.84 m). However, I cannot find the mass of said tree, and am trying to find it by multiplying density by the volume (530 m^3) because if p=m/V then p•V=m, but I cannot find the density of the tree, so...
  36. T

    How to determine the tank volume and power requirement?

    Hello everyone. I have to determine the tank volume and power requirement of a tank. The teacher has done it the following way, however, I don't understand the process.
  37. greg_rack

    Volume of a solid of rotation, obtained rotating a function around x=2

    At first, I inverted the function(##f^{-1}(x)=g(x)##) and calculated the volume through the integral: $$V=\pi\int_{0}^{4}[4-(2-g(x))^2]\ dx$$ but then I questioned myself if the same result could have been obtained without inverting the function. To find such a strategy, I proceeded as follows...
  38. M

    Biology Pharmacokinetics: Volume of Distribution and Total Body Clearance

    Hi, I was recently reading through Systems Kinetic Modeling notes and am struggling to understand the concepts of total volume of distribution and total body clearance. As far as I understand, the total volume of distribution ## V_c ## is the "volume of the compartment into which the...
  39. M

    Calculating Volume & Work: V1, V2, W

    First i calculate n: 500000 g / 32 g/mol = 15625 mol Then I calculate V1: (100000 Pa * V1)/288.15 K = 15625 mol * 8.31 J/mol.k so V1 = 374.145 m^3 I calculate V2: 100000¨ Pa * (374.145 m^3)^1.3 = 300000 Pa * (V2)^1.3 So V2 = 160.703 m^3 W = ((100000 Pa * 374.145 m^3)-(300000 Pa * 160.703...
  40. D

    Calculating Hot Air Balloon Volume & Lift

    Volume of hot air ballon V=((4/3 pi R^3)/2) + (1/3 pi h (R^2 + r^2 + Rh) = 2956.24 m3 Balloon: R=9m h=15m r=1m m = 750 kg H = 5000m T = 373 K p1 = 101300 Pa p2 = 50650 Pa M(air) = 0.029 kg/mol F = mg - 7350 N
  41. Krokodrile

    Engineering Final volume of a gas using the ideal gas equations

    Hey there! for this problem i try to use the combinate gas ecuation. First of all the values its necesary to have it in absolutes: 70 F = 527.67 K 90 F = 549.67 K The ecuation looks like: (200 psig) (1 ft^3)/529.67 K = (0.3 InHg) V2/549.67 K I can eliminate "K" but not psig with InHg for obtain...
  42. greg_rack

    Volume of a solid of revolution around the y-axis (def. integration)

    First, I calculated the inverse of ##y=e^x## since we're talking about y-axis rotations, which is of course ##x=lny##. Then, helping myself out with a drawing, I concluded that the total volume of the solid must've been: $$V=\pi\int_{0}^{1}1^2 \ dy \ +(\pi\int_{1}^{e}1^2 \ dy \ - \pi...
  43. George26

    Conservation of mass: control volume approach question

    Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...
  44. L

    Engineering Find the volume of a gas using Boyle's law

    Is this right go confused with the 37 degrees Q) pV = Constant pressure of a gas is ‘10’ (kPa) and the constant ‘37 degrees celcus’ = ‘0.6’, calculate the volume that the gas. pV = C C/p = V 0.6/10 = C V = 0.06
  45. J

    Finding area from work, pressure and volume

    So I basically took the integral and ended up with W=PVf-A(Vf^3)/3-PVi+A(Vf^3)/3 so 65.7=72*5.3-A(5.3)^3/3-72(2.4)+A(2.4)^3/3 But when I solve for A I get the wrong answer of 3.179 when the answer is suppose to be 5.05. I've checked my calculation with an algebra calculator too...
  46. W

    Low volume heard in phone calls, How to raise the volume?

    Hi, I have an LG K8 Android 2018. I am having trouble with the volume in conversations. I tried changing different settings without success. Any suggestions on how to raise the volume level during conversations? Is it a physical issue of wear and tear of the microphone, an issue with settings...
  47. AN630078

    Rates of change: surface area and volume of a sphere

    The surface area of the sphere is 4πr^2. dr/dt is given as 3cm^-1. dS/dt=dS/dr*dr/dt Differentiating 4πr^2 is dS/dr= 8πr dS/dt=8πr*3 dS/dt=24πr Given that r=5 dS/dt=24π*5=120 π The volume of the sphere is 4/3πr^3, differentiating which is dV/dr=4πr^2 dV/dt=dV/dr*dr/dt dV/dt= 4πr^2*3...
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