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. Timothy Schablin

    B Volume Compression in Cylinders: Does Diameter Affect Rate of Loss?

    Say we have 2 cylinders with the same volume capacities, but different radii, and a plunger to 'squeeze' the contents. We apply the same force to each plunger. Will the cylinder with the larger radii lose volume faster? Or will they be equal?
  2. Likith D

    Does Adjusting Potentiometer Resistance Affect Volume in Amplification Circuits?

    The above is a circuit i found on the net regarding amplification of volume. I needed to know if increasing the potentiometer resistance (between "cold" and "wiper"; terminal 1 and 2?) in the circuit would increase "volume" Also, i could use a potentiometer resistance ( between "cold" and...
  3. C

    Fluid Mechanics -- Volume flow rate

    Hey guys. I could use some explanation since I am new to FM: So my problem is the following one: Fluid flows with an average velocity 8 m/s in a pipe with diameter 3m. What is the volume flow rate? Now, I think the formula I got to use is Q= v.A Yet, I found my solution from a formula I found on...
  4. L

    Volume of a Solid using Cylindrical Shells

    Homework Statement Find the volume of the region bounded by the curves y=3x-2, y=6-x, and the x-axis when the region is rotated around the y-axis. Homework Equations Volume using cylindrical shells: 2π∫r(x)h(x)dx The Attempt at a Solution I graphed the curves and then found the x-intercept...
  5. Arman777

    I Size of an electron and Planck Volume.

    Theres something that bothers me, We claim that electron is a point particle.From that, Can we assume the volume the electron is ##(l_{h})^3## ( where ##l_h## is Planck length ) ? We know that every information can be described in bits like volume is ##(l_{h})^3## so, In every bit of...
  6. I

    B How can Greenland lose 269b tons/year and loose only 269km3?

    The density of ice is 920 kg/m3. Now let's calculate. m = 269 000 000 000 000 kg p = 920 kg/m3 ----------------------------- v=? V=m/p V=269 000 000 000 000 kg / 920 kg/m3 V = 292 391 304 347 m3 = 292 391 304.347 km3 v > 269 km3 *NOTE* I made a mistake in the title. I meant to write 269 km3...
  7. J

    Concentration of a salt produced by neutralization reaction

    Homework Statement 10.00 cm3 of 1.00 mol dm–3 sulfuric acid is fully neutralized by 20.00 cm3 of 1.00 mol dm–3 of sodium hydroxide. What is the concentration, in mol dm–3, of sodium sulfate solution produced by the reaction? A 0.33 B 0.50 C 0.67 D 1.00 Correct answer = A Homework Equations...
  8. P

    MHB Edin's question via email about volume by revolution.

    We should note that the two functions intersect at $\displaystyle \begin{align*} x = -\frac{1}{2} \end{align*}$ and $\displaystyle \begin{align*} x = 1 \end{align*}$. (a) Using the method of washers, the inner radius is $\displaystyle \begin{align*} 3 - \left( x + 1 \right) = 2 - x...
  9. harpazo

    MHB Volume for Triple Integral....2

    Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 4 - x^2, y = 4 - x^2, first octant I need help setting up the triple integral for the volume. I will do the rest.
  10. harpazo

    MHB Volume for Triple Integral

    Use a triple integral to find the volume of the solid bounded by the graphs of the equations. x = 4 - y^2, z = 0, z = x I need help setting up the triple integral for the volume. I will do the rest.
  11. Pushoam

    B Closed surface bounding a volume V

    Is a surface bounding a volume always a closed surface?
  12. Eric Willems

    Effects of high voltage & current on a large volume of water

    Hi, For a book that I’m writing, i need to know how to describe the following, if the situation described is ever possible, otherwise I'll have to come up with another scenario. A surge of high voltage electricity at a gas-insulated switchgear creates a flashover whose Breaker Current Failure...
  13. M

    MHB What is the volume of the shipping box?

    A shipping box is filled with pastry boxes. Each pastry box measures 1 cubic foot. The shipping box is 3 feet high. The bottom layer of the shipping box can fit 6 pastry boxes. What is the volume of the shipping box? Do I simply multiply 1 by 3 by 6 to get 18 cubic feet?
  14. O

    Control Volume of single expansion ramp nozzle (SERN)

    Hi guys, I need to determine the performance of a single expansion ramp nozzle (SERN) from CFD results with different nozzle pressure ratios (NPR). For some NPR the nozzle is overexpanded and for some underexpanded. Now the impact of the control volume definition on especially the axial thrust...
  15. Noaha

    Core volume of 1 phase transformer

    Homework Statement The flux density in a single phase core type symmetric(length=breadth=height) transformer is B and flux is Φ. Can we find out the volume of core of transformer if the height of limb is h? Homework Equations Φ = B * Cross sectional area The Attempt at a Solution Can we say...
  16. Another

    Need help finding the volume enclosed

    Homework Statement Find the volume in octane 1 enclosed. x + y + 2z = 2 2x + 2y +z = 4 ∫∫∫ dV Homework Equations - The Attempt at a Solution ∫∫∫ dv = [∫(0⇒2) [∫(2-2z)⇒(2-½z) [∫(2-2z-y)⇒(2-½z-y) dx] dy] dz] = [∫(0⇒2) [∫(2-2z)⇒(2-½z)...
  17. M

    Reynolds Transport Theorem and Volume calculation

    I cannot understand the the relation between Reynolds Transport Theorem and Volume Calculation. Volume calculation is an simple, straightforward process which, I think, have much connection between Reynolds Transport Theorem. We calculate volumes in thermodynamics, heat transfer and fluid...
  18. S

    Heat capacity at constant volume and density

    Hello! I encountered in a problem the terms heat capacity at constant volume and density (##n##) and heat capacity at constant chemical potential (##\mu##) and volume and I need to prove a relation between them. What is their definition? I thought that for the first one it would be...
  19. D

    Area between 2 curves, Volume around X and Y, Centroid

    g(x)= √(19x) = upper curve f(x)= 0.2x^2 = lower curve Firstly, I found the point of intersection, which would later give the upper values for x and y. x=7.802 y=12.174 Then I found the area under g(x) and took away the area under f(x) to get the area between the curves. 31.67 units^2 This is...
  20. davidge

    I Is the Notation for Coordinate Transformation in Relativity Problematic?

    In a change of coordinate system we have ##dx^\mu = (\partial x^\mu / \partial \xi^{\kappa})d \xi^{\kappa}##, where the term in round brackets is the Jacobian. That notation implies a sum over all values that ##\kappa## can take. This don't tell us that it's an alternating sum for the case of...
  21. 6

    MHB Therefore, the volume of the rectangular prism is 84 units cubed.

    What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?
  22. W

    Mole balance issue with volume division

    Homework Statement Here we divide the mole balance by the volume ##4*\pi## ##*## r2##*##dr and take lim as dr->0(standard procedure) 1) How exactly he makes the transition from equation from 6 to 7? Exercise #2(see below please) Solution for Problem#2 2)Why does he divide here by...
  23. Vitani11

    Calculate the volume integral of divergence over a sphere

    Homework Statement For the vector field F(r) = Ar3e-ar2rˆ+Br-3θ^ calculate the volume integral of the divergence over a sphere of radius R, centered at the origin. Homework Equations Volume of sphere V= ∫∫∫dV = ∫∫∫r2sinθdrdθdφ Force F(r) = Ar3e-ar2rˆ+Br-3θ^ where ^ denote basis (unit vectors)...
  24. T

    Calculating Gasoline Tank Depth and Volume

    Homework Statement (a) A rectangular gasoline tank can hold 39.0 kg of gasoline when full. What is the depth of the tank if it is 0.450 m wide by 0.900 m long? m (b) What is the volume of the tank? (It is suitable for a passenger car.) gal Homework Equations Density of gas=719.7=mass/volume...
  25. David23454

    Expression for volume charge density of a sphere

    Homework Statement I'm having a bit of trouble with this problem: "A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r≤R) is E(r)=r^4Emax/R^4. a. What is Emax in terms of Q and R? b. Find an expression for the volume charge density ρ(r)...
  26. U

    B Integrating to find surface area/volume of hemisphere

    To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...
  27. D

    MHB Calculate Sphere Volume Using (4.0/3.0) Division

    Given sphereRadius and piVal, compute the volume of a sphere and assign to sphereVolume. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. public class SphereVolumeCalculator { public static void main (String [] args) { double piVal...
  28. wasup23

    I Introducing two identical containers with different gasses

    If you have two different containers filled with two different gasses at the same temperature, would they have less pressure when connected to each other? Dalton's law states that each of the gases behave independently when it comes to pressure as they fill the space as if they were the only gas...
  29. N

    B Do neutron stars have a minimum volume?

    Do neutron stars have a minimum volume? Anything "in the way" of perhaps baseball sized neutron star? Or would something like that be an impossibility? How neat to have one in a laboratory...or not lol
  30. R

    Calculating Pressure and Volume for an Air Cannon Tank

    Morning all, I am working on a Air Cannon Project and have hit a stumbling block. I am trying to work out what tank pressure and volume I would need to project a 1.4kg mass to 83m/s when it leaves the barrel. The barrel the mass will travel down is 4 meters long and 6inch in diameter, would...
  31. L

    Laser Beam Diameter which Minimizes Volume?

    Homework Statement Consider a 10 meter long gas column. We interrogate the gas molecules with a HeNe laser (lambda=633nm) at the minimum possible gas volume. If we focus the beam tightly, it will eventually diverge and the sampled gas volume will increase. Consider a minimum beam diameter D...
  32. alan

    Temperature and volume fraction of a liquid mixture

    I have known the interaction parameter of a certain liquid mixture which has the phase behaviour can be described by the lattice model. , is it possible for us to know the temperature at the critical point? Besides, if we know the temperature at the critical point, can the volume fraction of...
  33. V

    Find the Magnitude of Theta to Maximize Volume of a Cone

    Homework Statement A sector with central angle θ is cut from a circle of radius R = 6 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of θ such that the volume of the cone is a maximum. Homework Equations Volume of a Cone = ⅓ * π * r2 * h Area of a...
  34. K

    Volume of water required to cool thermal/nuclear plants?

    Homework Statement In the year 2004 the USA produced 1787 TWh of electrical energy in conventional thermal plants and 476 TWh in nuclear plants. Assuming 30% efficiency for nuclear plants and 40% for conventional thermal plants, determine the (annual) volume of cooling water required to cool...
  35. Mictlantecuhtli

    Expressing surface charge density as volume charge density

    I'm working on this: When I consider a disc with radius ##a## and total charge ##Q## uniformly distributed (placed in the XY plane and centered at the origin) and determine the volume charge density in cylindrical coordinates, I have assumed is of the form ##\rho=A \delta (z) U(R-r)##, (##U## is...
  36. Jovy

    How Do You Calculate the Volume of a Torus Formed by Revolving a Circle?

    Homework Statement A torus is formed by revolving the region bounded by the circle ##x^2+ y^2= 1## about the line x =2 Find the volume of this “doughnut-shaped” solid. (Hint: The integral ##{\int_{-1}^1} \sqrt{1 -x^2} dx## represents the area of a semicircle.) 2. Homework Equations...
  37. C

    I Measuring the Volume of a Cup: A Scientific Analysis

    If I submerge a cup in a graduated cylinder filled with water, will the change of the water line show me the volume of the cup? Or is this not the case? I am in an argument with a friend, he believes that the volume of the cup could be found by holding the top of the cup right about the water...
  38. Jovy

    Finding Volume of Rotated Region Bounded by Equations

    Homework Statement Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y =4. $$y=\frac 3 {1+x},~ y=0,~ x=0,~x=3$$ Homework Equations $$V= \int_a^b ([R(x)]^2-[r(x)]^2)dx$$ The Attempt at a Solution I understand how to use the...
  39. rebc

    Calculating the volume of a nucleus

    Homework Statement I am to calculate the density of a nucleus, say, of Iron, with mass 55.845 amu. Homework Equations see below The Attempt at a Solution I come to notice that all elements have the same value for the volume if I use the formula: $$mass=m=m_{amu}(1.66\times10^{-27}kg/1u)$$...
  40. T

    How Do You Calculate the Volume of a Parabolic Roadbed?

    Homework Statement Determine the number of cubic yards of crushed rock necessary to make a roadbed with the cross-section shown below, if the road is to be 1/4 mile − long. Assume that the crown of the pavement is an arc of a parabola, with its vertex at the top center. Be careful with units...
  41. B

    Air volume in the tank, volume vs pressure

    New to forum Most air tanks are categorized on volume of air they hold . The question I have is this that a 5 gal air tank that holds 160 psi , is it equivalent to a tank that holds 2.5 gal of air at 320 PSI ? if not then is there a formula to figure this ratio . Thanks
  42. D

    Volume occupied a single molecule of water.

    Homework Statement My problem includes answers from previous problems that are to be used as data in this problem so I will state the previous problems and the answers but not their solutions because I have solved them and they are pretty clear to me. So, I will be only posting the solution to...
  43. D

    B Do particles actually have a volume?

    You often hear "most of everything is made up of empty space", referring to the idea that atoms only have mass in their nucleus. It seems to me that this is trying to explain physics in terms of everyday intuition, rather than the other way around. Specifically we have this intuitive notion of...
  44. Neo Tran

    Number of secondaries generated in a volume MCNP?

    Hello everyone, I am having a problem with MCNP. My question is how to get number of secondaries in a certain volume. For example I have a neutron beam bombarded Pb target, and I want to count all of proton formed in the target. I considered tally F4, but the unit is 1/cm**2. Who can explain the...
  45. G

    Entropy of ideal gas: Volume it *has* or is *allowed* to have?

    Hi. If an ideal gas of ##N## particles is allowed to expand isothermically to double its initial volume, the entropy increase is $$\Delta S=N\cdot k_B \cdot \log\left(\frac{V_f}{V_i}\right)=N\cdot k_B \cdot \log\left(\frac{2V}{V}\right)=N\cdot k_B \cdot \log\left(2\right)\enspace .$$ This can...
  46. M

    Express volume expansivity in terms of density

    Homework Statement Express volume expansivity (B) in terms of density (ρ) and its partial derivatives Homework Equations B = (1/V) (dV/dT) V = m/ρ The Attempt at a Solution I have only managed to substitute m/ρ into the expansivity equation. Don't really understand how to manipulate the...
  47. I

    Thermodynamics.... Constant volume pressure of combustion

    Hi guys, 42 year old engine hobbyist here, not a student. I've had great luck figuring out my questions in this portion of the forum in the past and look forward to your input. Keep in mind that I'm not formally educated, so if it's possible to dumb something down a bit I'd appreciate it.1...
  48. Dilemma

    Finding the volume - Polar coordinates

    Hello everyone, 1. Homework Statement Question : Find the volume of the region which remains inside the cyclinder x 2 + y 2 = 2y, and is bounded from above by the paraboloid surface x 2 + y 2 + z = 1 and from below by the plane z = 0 Homework Equations The Attempt at a Solution This looks...
  49. R

    I How to solve for the volume of the universe / redshift

    Hey ! i am having this question to be answered , i am new to the cosmology studies and still a bit confused about some formulas. the question is: (a) The greatest redshift known corresponds to the cosmic microwave background (CMB, CBR) at redshift z 1100 (although the redshift is obtained...
  50. karush

    MHB S6.793.12.4.33 Find the volume of the parallelepiped

    $\tiny{s6.793.12.4.33}$ $\textsf{ Find the volume of the parallelepiped determined by the vectors, a b and c}$ $ a =\langle 6, 3, -1\rangle \, b =\langle 0, 1, 2 \rangle \, c =\langle 4, -2, 5 \rangle $ $\textsf{The volumn of the parallelepiped determined by the vectors }\\$ $\textsf{ $a...
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