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.
I have very large data sets:
coins & amount
i.e. {10 & 11, 9 & 7, 8 & 9, 4 & 5, 3 & 1} graphed would show greater volume to the left side while {1 & 0, 2 & 3, 2 & 1, 4 & 6, 9 & 10} would reflect greater volume on the right, and {1 & 4, 2 & 3, 12 & 10, 4 & 4, 3 & 2} would reflect a surge in the...
Homework Statement
The top of a rubber band bushing is designed to absorb vibrations in an automobile is the surface of a revolution generated by revolving the curve z = (0.5y^2) + 2
for (0<= y <= 3) in the yz plane about the z axis.
use the shell method to find its volume...
Question: What volume of a 0.835 M solution of Na2SO4 do you have if there are 0.0534 mol of Na+ present in the solution?
What I did: Since we have 0.0534 moles of Na+ ions in the Na2SO4 molecule, I used that for the equation. Since 0.0534 moles is in a 1:1 ratio with Na2SO4 I can conclude we...
Homework Statement
according to the model ans, the volime of oxygen produced is 25x 24 dm^3 ...
where does the 25 come from ??
or someone can show me other step of getting the ans ? thanks in advance!
according to the model ans, the volime of oxygen produced is 25x 24...
Homework Statement
A 1-cm3 air bubble at a depth of 141 meters and at a temperature of 4 degrees Celsius rises to the surface of the lake where the temperature is 13.1 degrees Celsius, to the nearest tenth of a cm3, what is its new volume?Homework Equations
P1V1/T1=P2V2/T2The Attempt at a...
If a helium-filled balloon initially at room temperature is placed in a freezer, will its volume increase, decrease, or remain the same?
The Attempt at a Solution
If you decrease the T of a vessel filled with gas, its molecules will have less kinetic energy, and the pressure inside the...
From browsing this website I have formed an opinion that people in here don't like when someone brings up information that they heard in a movie..
Well this is more along the lines of a question that arose from watching a movie..
With Sandra Bullock, forgot the name..
Dialogue went something...
I am no english native speaker, sorry if something is a little confuse.
I was swimming, and then I realized that when I let the air go our of my lungs I sink. I though this might be because of changes in the volume of my body while holding air or letting it go. So I hold as much air as I...
1.find tthe volume solid generated by revolving the region bounded y=sqrt x and the ;lines y=1, x=4 about the line y=1
2. using simpson rule witj n=4 to aproximate int from 0 to 1 1 over 1-x power 2 dx
The Volume of an atom comes from its electrons and mass of an atom comes from its nucleons. I don't understand why?
Any one can explain it please?
Thanks in advance
In 2 dimensions
given a scalar field f(x,y)
is possible to compute the line integral ##\int f ds## and area integral ##\iint f d^2A##.
In 3D, given a scalar field f(x,y,z)
is possible to compute the surface integral ##\iint f d^2S## and the volume integral too ##\iiint f d^3V##...
Y=x^(2/3) and y=x^2 rotated about the x=4.
First I equate the equations giving me x=0,-1,1. The problem is I have exactly 2 graphs that are symmetric in respect to the y axis. N I have not encountered a problem in stewart dealing with this.
I know that the volume on the right side of the...
Hey
I am a physics student, and not so familiar with chemistry. I have a huge problem, because I have to find the following 3 values for liquid isopropanol:
1. The specific heat capacity at constant volume
2. The specific heat capacity at constant pressure
3. Volumetric Isobaric...
Say for example you have take a sample of 500ml from a bulk saline solution (NaCl and H20). If you know that for every 100 grams of water there is 10 grams of NaCl, can you calculate the amount of NaCl in 500ml of the final mixture?
Homework Statement
A dam has a rectangular base 1500 meters long and 140 meters wide. Its cross-section is shown in the figure. (The Grand Coulee Dam in Washington state is roughly this size.) By slicing horizontally, set up and evaluate a definite integral giving the volume of material used...
Hello .
I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below
Now i should find the Perimeter, Volume and Surface of this figure .
Lengths are all 5 cm, Can somebody find and write the
Permiter,volume and surface for this figure please it's urgent...
Hi everyone,
I'm a bit confused with this question.
An airline demands that all carry-on bags must have length + width + height at most 90cm. What is the maximum volume of a carry-on bag? How do you know this is the maximum?
[Note: You can assume that the airline technically mean "all carry...
calculate the volume obtained when the area bounded by y=e^x, x=1, y=1, is rotated around x=4. use shell method. Can I see your integral?
My teacher gave me the first integral. I found the second one here: BUT: the two do not give the same numerical result:
integral of pi((4-lnx)^2-9) FROM 1...
So this is the problem that I am working on. It is a woosh bottle where I am inputting 70% isopropyl alcohol, closing the top and waiting for the alcohol to evaporate. This mixture is then ignited to generate a flame. My job for this project is to calculate the maximum volume of 70% isopropyl...
Hi:
I have been working in this Project for a while now and I would like to share the results with you. Still needs some improvements; but it appears to be working fine so far. Please let me know your suggestions and ideas.
Thanks.
Homework Statement
By using triple integral, find the volume of the tetrahedron bounded by the coordinate planes and the plane 2x+3y+2z=6.Homework Equations
Volume= ∫vdv=∫∫∫dxdydz
The Attempt at a Solution
find intercepts of the plane on the axes,
x-intercept=3
y-intercept=2...
Homework Statement
Find the volume of the region enclosed by z = 1 - y^2 and z = y^2 - 1 for x lying between 0 and 2 inclusive.
Homework Equations
The Attempt at a Solution
I know that the y bounds are from -1 to 1, where the parabolas meet. x bounds are from 0 to 2. So would...
Homework Statement
Find surface and volume charge densities. Deduce electric field.
Homework Equations
The Attempt at a Solution
Volume charge density:
\epsilon_0 \epsilon_r \nabla . \vec E = \rho_f
Using ##\vec P = \chi \epsilon_0 \vec E = (\epsilon_r -1)\epsilon_0 \vec E##...
Hi, I have a book that makes the equality.
\vec{B}dV = (\vec{e_1}B_1 + \vec{e_2}B_2 + \vec{e_1}B_2)dx_1 dx_2 dx_3 \\[1ex]
= dx_1 \vec{e}_1(B_1 dx_2 dx_3 ) + dx_2 \vec{e}_2(B_2 dx_1 dx_3 ) + dx_3 \vec{e}_3 (B_3 dx_1 dx_2) = (\vec{B}\cdot d\vec{S}) d\vec{l}.
I'm a bit confused as to how it...
Today in my chemistry class, the teacher said:
Is it true? If yes I have a doubt. 0 vloume means the matter will demolish right? Then how will the mass of the demolished matter be conserved according to Law of conservation of mass?
Homework Statement
A standard mercury thermometer consists of a hollow glass cylinder, the stem, attached to a bulb filled with mercury. As the temperature of the thermometer changes, the mercury expands (or contracts) and the height of the mercury column in the stem changes. Marks are made on...
A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then it's volume is
I keep on getting 18 root 3. But the answer is 36 root 3.
Could I get some help?
Thanks.
Homework Statement
Hello!
English is not my native language so I hope the terminology is right.
Q:
Find the volume generated by the curve y=1/x+2, positive x- and y-axis and the line x=1.
Calculate the volume obtained by rotation around the:
a) x-axis
b) y-axis
Homework...
https://www.physicsforums.com/attachments/69284Homework Statement
i have done the part a, for b , i use the key in the (circled part equation ) into calculator .. my ans is also different form the ans given. is my concept correct by the way?
Homework Equations
The Attempt at a...
Homework Statement
Use a double integral to find the volume of the indicated solid.
Homework Equations
The Attempt at a Solution
I can't find what I did wrong, it seems like a simple problem...
$$\int_0^2 \int_0^x (4-y^{2})dydx=\int_0^2 4x-\frac{x^{3}}{3}dx$$...
Homework Statement
Let ##A\subset E^n## be a set with volume and ##f:A\to\mathbb{R}## a continuous function. Show that if the set ##\{x\in A:f(x)=0\}## has volume zero, then the set ##\{x\in A:f(x)>0\}## has volume.
Homework Equations
None
The Attempt at a Solution
A proposition...
1. The problem statement, all vbles and given/known data
So I'm going throught the Nova Physics book and I'm wondering if there's a mistake in calculation. The question reads: How much volume does 0.4kg of oxygen gas take up at T= 27 degrees Celsius and P= 12 atm (gas constant R = 0.0821 L...
Homework Statement
Let ##A\subset E^n## and let ##f:A\to E^m.## Consider the condition that there exist some ##M\in\mathbb{R}## such that ##d(f(x),f(y))\le Md(x,y)## for all ##x,y\in A.##
Show that if the condition is satisfied, if ##m=n##, and ##\text{vol}(A)=0##, then...
Homework Statement
Whats the stock solution volume required to prepare 100ml of a NaHCO3 solution 5g/L using a stock solution of NaHCO3 30g/L.
Homework Equations
M1*V1 = M2*V2
M = Molarity = mols/L
The Attempt at a Solution
NaHCO3 = 84g/mol
5g NaHCO3 = 0.0595238095238095mol
30g NaHCO3 =...
Homework Statement
Here is the problem: You are worried that your -80C freezer is on the fritz. Unfortunately you do not have a thermometer. You do have a balloon. so, you blow up the balloon and measure that it has a diameter of 10cm when at 25C. you put it in the freezer, let it come to...
Homework Statement
Find the volume enclosed by the cone x^{2}+y^{2}=z^{2}
and the plane 2z-y-2=0.
Homework Equations
\int\int\int dV
The Attempt at a Solution
In the image Cono=Cone and Plano=Plane
Hello,
I'm not sure if I'm approaching this the right way, but essentially I used the definition of volume expansivity and a result for the molar volume of an ideal solution to get my expression, so my result is that the claim is wrong. Am I going about this one correctly?
1. estimate the fermi energy for lithium... the crystal structure of lithium is a bcc with a unit cell size of 3.5*10^-10 m
[b]i need n, which equals N / V. if i divide by per atom, then i get (N/atom) / (V/atom) = valance / (V/atom). my question is how to get the volume per atom...
please tell me if i did this correctly:
task: I'm trying to divide the differential dA by dV
where.. dA = differential surface area of a sphere, dV = differential volume of a sphere
dA=8\pirdr
dV=4\pir2dr
so then dA/dV= 2/r
Also, if i treat this as a derivative, then would...
Hello,
I am working on the derivation that proves that the partial molar volume of an ideal gas is equal to the molar volume of an ideal gas.
I am following up to the point in the textbook where they set
(∂n/∂ni)nj = 1
where ni is the number of of moles of species i, and nj is the...
If you have a charged solid sphere with uniform volume charge density ρ, then the total charge on the sphere is
Q = ρ*4/3*∏*R^3 , where R is the radius of the sphere.
Now...
Homework Statement
I know how to apply the linear momentum equation for the control volume, but I am not sure why the V2 (velocity of flow from section 2) is V*cos(60).
The only reason I can see is the velocity being constant. And since there are two outlet with equal area, the velocity is...
Hi,
Sorry for the semi-book here
I am working on a project where I am mixing h-BN nanoparticles into a polymer resin to try to tailor the thermal conductivity and dielectric strength of the resulting composite.
Admittedly I am not very well versed when it comes to materials science...
Hi,
I just need these solutions checked.
Thank you in advance!
Consider the region bounded by the following curves ##y=x-3, y=5-x, \text{and}\ y=3##:
1.) set up an integral expression that would give the area of the region of y as a function of x:
##y = x-3 = 5-x##
##x + x - 3 -...
Homework Statement
Let V be the volume of the solid enclosed by the sphere x^2 + y^2 + z^2 - 2z = 0 ,
and the hemisphere x^2 + y^2 + z^2 = 9 , z ≥ 0. Find VHomework Equations
Using spherical coordinates:
x^2 + y^2 + z^2 = ρ^2
z = ρcos(ø)
The Attempt at a Solution
So I changed both of them to...