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.
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...
(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...
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...)
I tried integrating the 4-volume of a 4-hemisphere, that is, $$\int^{R}_{0} \frac{4}{3} \pi r^3 dw$$ (along w-axis), since ##r## is proportional to ##w##, where ##r=\frac{w}{R} R##, ##r=w##, thus the integral becomes $$\int^{R}_{0} \frac{4}{3} \pi w^3 dw = \frac{\pi}{3} R^4$$ The volume of a 4-D...
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...
First of all, I don't think the question was clear enough. Therefore, I had to assume they are referring to the volume of the unit cell.
V=a^3, side length a
aBCC=2R√2, aFCC=4√3/3R
%change=(VFCC-VBCC)/VBCC
I thought this was right until I checked with others who did this:
so the only...
Homework Statement:: Oil Lamp ( Paraffin help )
Relevant Equations:: Not sure what to write here
HI folks,
I'm trying to make an oil lamp from an old Vodka bottle.
The bottle is the usual 750ml and is in a skull shape bottle. ( maybe you know it )
Anyhow I have all the materials and almost...
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.
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
Some notation:
- the difference between the heights of mercury, which is effectively the height of the mercury in the open end of the tube is ##h_{diff}##
- the volume of gas inside the sealed off end is ##V_{inside}##
- the volume of gas when let outside, "normal volume", is ##V_{outside}##
-...
Summary:: Can anyone help me with this 3d Volumetric Strain and Volume Change. The is question is attached as a document below with the question and my attempt at the answer
All questions and attempted answers are in the attached file below
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...
Spatial slices of the Robertson-Walker metrics are maximally symmetric so they must have a constant curvature. Is it true that in three Riemannian dimensions that a constant curvature scalar determines whether the volume is finite or infinite? Carroll seems to have given a counter-example for...
Hi,
If I had a volume of Brown's gas at 20°C / 1atm, what would the expected volume [of the resultant steam] be immediately after it was ignited?
Thanks!
Bob
Homework Statement:: How to control volume by hovering and scrolling anywhere in Mac Menu Bar
Relevant Equations:: none
Hi,
I use both Mac's and pc's. Mac's are great but here's one thing
I can do in my pc's that I have not been able to find how to do
in my Mac.
In my pc's (Win7, Win10)...
In this explanation we need to involve the Dirac delta functions(maybe) but I clearly have a difficulty in understanding it can some one explain me the whole concept of constant or non constant volume charge density.
We know that we humans have roughly 5 liters of blood circulating in our body. The volume also may be varying. We also know that its volume is tightly regulated and multiple organs are involved in it.
My question is, how we calculated that we have 5 liters of blood? Is it an approximation or...
Hello folks, a recent theoretical discussion with a materials engineer has left my head spinning, this sort of thing is beyond me but I am curious if any of the clever folks on here could solve my problem.
I want to find the Force and Energy applied by my Indenter within the following...
I'm assuming the way to go about it is to integrate in spherical coordinates, but I have no idea what the bounds would be since the bottom edges of the square pyramid are some function of r, theta, and phi.
the equation of a parabola that is obtained by taking a cross-section passing through the center of the paraboloid is ##y = ax^2##
breaking the paraboloid into cylinders of height ##(dy)## the volume of each tiny cylinder is given by ##\pi x^2 dy##
since ##y = ax^2## we have ##\pi (y/a) dy##...
The question is: If the compression ratio of car engines is increased by 10% (from 10 to 11), estimate the volume reduction in annual CO2 emission. Assume there are 30 million cars each consuming one cubic meter of fuel annually.
The question is looking for a rough estimate for an answer.
I...
Hi,
I tried to do this question in two different approaches one of them was using the equation PV=mRT where I got the right answer which is 4.305 m**2. However, I tried using this Density = Mass/Volume, where I substituted Denisity= 1.225 and Mass equals 5kg to get the volume as 4.08.
Can...
Made an attempt at this Q but I'm unsure on how to do part c) or if I had even done part a) and b) right
What difference does it make to the volume flow rate equation when the valve goes from open to closed?
Any help would be appreciated! Thanks
The answer to the primary question in the summary is the first step in seeking an answer to a more complicated question I plan to post in a separate thread later. This more complicated question is a consequence of the thread...
Am I right to assume that the equivalents for phenyl magnesium bromide would be 3 (magnesium, bromobenzene and ether (?)) And the number for 2-phenyl-propanal 1 as it says "...was added to 2-phenylpropionaldehyde" which is the same thing as 2-phenylpropanal? I don't know if I understood this...
Robert Boyle's law states that at constant temperature, the pressure of fixed amount ( i-e number of moles n) of gas varies inversely with its volume. Mathematically, it can be written as $p ∝ \frac1V $(at constant T and n) $\Rightarrow p = k_1 \times \frac1V $ where $k_1$is a proportionality...
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...
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...
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...
1#Find the area of the region, enclosed by:
2#Find the area of the region bounded by:
3#in the region limited by:
find the solid volume of revolution that is generated by rotating that region about the x axis
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...
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This was a problem introduced during my classical electrodynamics course.
I am not 100% sure, but I think I've solved up to problems (a) and (b) as...
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...
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...
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...
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##.
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...
Hi to everyone,
do you know the "One World Trade Center"?
Well, I've to calculate two things about it:
-The volume, according to its particular shape
-The surface of the glass plates which cover the whole structure
Searching on internet i found two dimensions:
1) Total height without...
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...