Volume Definition and 1000 Threads

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...

hi every body Consider we have a null hypersurface. how we can calculate volume element on it?

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...

Is this so? I cannot think of a counter-example and it is too general a statement to prove.

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...

Say that we have a salt solution does the volume of the solution change after when the salt is ionized and equilibrium is achieved ??

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?

I do not know how to formulate formulas on this forum so I just wrote it neatly on a piece of paper and linked it. http://puu.sh/8fwXr.jpg Thankss.

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...

I'm having some trouble with this problem: Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= 6(4-x)^(-1/3) and the x-axis on the interval [0,4) is revolved avout the y-axis. How would I be able to tell whether to use the shell, disk, or...

Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= the square root of ((x+3)/(x^3)) and the x-axis on the interval [1,infinity) is revolved around the x-axis. I tried using the disk method: pi* (sqrt(((x+3)/(x^3)))^2 Then I think I have to...

Homework Statement Find the volume of the solid generated by rotating the region enclosed by y=\frac{1}{1+x^2} , x=-1,x=1 and y=0 about the line y=2 Homework Equations pi(outer radius)^2-pi(inner radius)^2 The Attempt at a Solution Since i am rotating around a horizontal line i figured...

Homework Statement f(x)=\frac{1}{81}*x^4-\frac{5}{9}*x^2+4 The tangent in Point P(6|0) when rotated around the y-Axis gives the Shape of the Squeezer. The bottom is at y=-5, the top at y=0 The Attempt at a Solution First I calculated the tangent and got t: y=4x-24 Then I converted that to...

I can compute the area of the rectangle formed by Δx and Δy simply by product ΔxΔy. Now, how can I to compute the area in gray given Δr and Δθ? Also, I can to compute the volume of a parallelepiped formed by Δx, Δy and Δz, simply multiplicand ΔxΔyΔz. But, how can I compute the volume...

A cone's volume with height ##x## and radius ##y## is ##1/3## of the volume of a cylinder with height ##x## and radius ##y##.I was trying to visualize it in my head and struggled a bit.Take a rectangle triangle with height ##x## and the other side of length ##y## which isn't the hypothenuse ...

A cylindrical container of height 1 m and diameter 0.5 m is partially filled with apple juice. When the container is lying on its side, the juice level at the deepest point is 37.5 cm (three eighths of a meter from the bottom of the cylinder is full). What is the liquid level after the container...

Homework Statement The surface of a double lobed cam are modeled by the inequalities: \frac{1}{4}\leqr\leq\frac{1}{2}(1+cos2θ) and -9/(4(x2+y2+9)) ≤ z ≤ 9/(4(x2+y2+9)) Find the volume of the steel in the cam. Homework Equations The Attempt at a Solution I know I...

Homework Statement Set up an integral to find the volume of the tetrahedron with vertices (0,0,0), (2,1,0), (0,2,0), (0,0,3).Homework Equations The Attempt at a Solution My method of solving this involves using a triple integral. The first step is deciding on the bounds of the triple integral...

Im confused by a concept i have run across in Griffiths electrodynamics. E_{out} - E_{in} = \frac{\sigma_{free}}{\epsilon_0} However, in the case of a uniform, circular charge density, \vec{E_{in}} = \frac{\rho r}{3\epsilon_0}\hat{r} \vec{E_{out}} = \frac{\rho R^3}{3\epsilon_0...

Hello Homework Statement Show that for an ideal gas: n(E)dE=2πn/(kπT)3/2 *E1/2 exp(-E/kT) dE where n(E) is the number of particles for each element of volume whose energy is between E and E+dE Homework Equations The Attempt at a Solution Really don't know where to start...