Volume Definition and 1000 Threads

Homework Statement A rectangle with a perimeter of 40 cm is rotated around one of its sides creating a right cylinder. What is the largest possible volume for this cylinder? Homework Equations Volume of a cylinder= pi*r^2*h Perimeter of a rectangle= 2x + 2L The Attempt at a Solution I know...

Homework Statement what is G and γ mean here ? Homework EquationsThe Attempt at a Solution

I'm using the textbook Electricity and Magnetism by Purcell. In the section about continuous charge distributions I found the following formula \mathbf{E}(x,y,z)= \frac{1}{4\pi\epsilon_0 } \int \frac{\rho(x',y',z')\boldsymbol{\hat r} dx'dy'dz'}{r^{2}} . It's stated that (x,y,z) is fixed...

Find the volume of the solid generated by rotating the region of the x-y plane between the line Y=4,the curve Y=3sin(x)+1 on the interval [-pi/2,3pi/2] about the line Y=4Hi I am having trouble setting up this problem my guess for the integral would be from -pi/2 to 3pi/2 of (4-3sinx+1)^2 because...

The volume enclosed by rotating the segment of the curve $y = \frac{1}{2}|x-1|$ between $x = 0$ and $x = 2$ about the $x$-axis is equal to: Is it this simple? Since $x \ge 0$ it's $\frac{\pi}{2} \int_0^2 (\sqrt{(x-1)^2})^2\, dx = \frac{\pi}{3}.$

In another thread https://www.physicsforums.com/threads/why-does-the-universe-have-no-net-charge.843865/page-2#post-5326092 I was amazed to learn the following from a post by bcrowell: "You can't get the total mass of the system by adding up the masses of all its parts." The reason for this is...

Consider the solid in three dimensions that is formed when the graph of a function $f(x)$, with $f(x) \ge  0$ for all $x \in [a, b]$, is revolved around the $x$-axis on the segment $x \in [a, b]$. Derive the following formula for the volume $V$ of this solid: $V = \pi\int_a^b f^2(x)dx$. Use...

Homework Statement Hello all! I need a little bit of help with my physics homework! It asks me to calculate the change in volume produced by the piston, and it gives me the equation: ∆V= Ax∆dHomework EquationsThe Attempt at a Solution Now I know that A= 1x 10-^16m^2 And ∆d=1700nm My only...

Homework Statement The reaction between aluminium powder and anhydrous barium nitrate is used as the propellant in some fireworks. The metal oxides and nitrogen are the only products. Which volume of nitrogen, measured under room conditions, is produced when 0.783 g of anhydrous barium nitrate...

Homework Statement 1.0 mA proton beam accelerated through potential difference of 1 keV. Determine the volume charge density of the beam after acceleration assuming uniform current distribution within diameter of 5mm, with zero current outside of this. Particle starting from rest. Final answer...

Homework Statement What is the volume of a solid formed by the area trapped between y= -x^2 and y= -2x rotated 360° around x-axis? Homework Equations V = ∫A(x)dx The Attempt at a Solution y=y -x^2 = -2x x^2 -2x = 0 x(x-2) = 0 This means that the two functions cross at x = 0 and x = 2 From x...

Hello, Surfing across the internet, I learned that the volume of a sphere in n dimensions can be expressed by V(n) = (Π^(n/2)) / Γ((n/2)+1), where n is the number of dimensions we are considering But if we consider n=0, then we get 1. So, how do we interpret this? I mean what does volume in zero...

Homework Statement There is a block of wood floating on the surface of a body of water, with a ball attached to the bottom of the block by a string. I am asked to find the volume of the ball given the tension in the string. We also know the volume of the wood block from an earlier problem if...

Homework Statement An object of 985 kg/cm^3 density is placed in water, which has a density of 1000 kg/m^3. What percentage of the object will be floating above the water? Homework EquationsThe Attempt at a Solution 985/1000 = .985, or 98.5%. 100 - 98.5 = 1.5%. Therefore: 1.5% of this object...

Homework Statement A sample containing 3.65 mol of a monatomic ideal gas is heated from 289K to 458K, and the entropy remains constant. If the initial volume of the sample was 0.0980m^2, by what factor did the pressure increase or decrease during this process? Homework EquationsThe Attempt at...

I've read in my texts that the there are two kinds of Molar Specific Heat Capacities for gases: 1. Molar Specific Heat Capacity at constant Volume ----- ##C_v## 2. Molar Specific Heat Capacity at constant Pressure ---- ##C_p## And in case of Constant temperature there is no point in...

Homework Statement Two moles of an ideal gas undergo a reversible isothermal expansion from 3.37×10−2m3 to 4.29×10−2m3 at a temperature of 29.6 ∘C. What is the change in entropy ΔS of the gas? Homework Equations pV=nRT The Attempt at a Solution W=∫V2V1pdV, I don't know how to use this...

On this picture we see a octagonal dome. I am trying to calculate the volume of this object by integral calculus but I can't find a way. How would you calculate this? https://dl.dropboxusercontent.com/u/17974596/Sk%C3%A6rmbillede%202015-12-17%20kl.%2002.14.48.png I am majoring in math-econ but...

Ok so i know the equation for the volume of a cylinder and the equation for calculating the radius. But when calculating the radius does the volume need to be converted into cubic inches or can it stay as imperial fluid ounces. Thanks

I just joined to ask this question... I was imagining a sphere made of mirrors inside it and shooting a light to the inside (assuming none of it would escape back through the same hole). Once light enters, it will forever bounce inside the sphere. So my question is, will there be a limit of...

Homework Statement A container of volume 2V is divided into two compartments of equal volume by an impenetrable wall. One of the compartments is filled with an ideal gas with N particles. The gas is in equilibrium and has a temperature T. How does the total energy, the entropy, the temperature...

Dear PF Forum, A: 1 mole O2 is roughly 32 grams? 1 mole ozone is roughly 48 grams? 1 mole CO2 is roughly 46 grams? Considering there are isotopes --------------------------------------------------------------- B: Do, at the same temperature and pressure, 1 mole CO2 and 1 mole O2 have the...

Homework Statement Hypothesize a human with a weight of: 61.14 kg (not an abnormal specimen in this wise). density of a human body: 985 kg/m^3Homework Equations What is the volume in cubic meters of such a hypothetical person? The Attempt at a Solution The mass of this person is determined...

Figure P6.95 provides steady-state test data for a control volume in which two entering streams of air mix to form a single exiting stream. Stray heat transfer and kinetic and potential energy effects are negligible. A hard-to-read photocopy of the data sheet indicates that the pressure of the...

Homework Statement "[Find the volume of a] solid whose base is the region bounded by the curves (y = x2) and y = 2 - x2 and whose cross sections through the solid perpendicular to the x-axis are squares." Homework Equations A(f(x)) = f(x)2 V = ∫(A(f(x))dx Image of problem...

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A piece of wood with a density of 730 kg/m3 is tied with a string to the bottom of a water-filled flask. The wood is completely immersed, and the tension in the string is 1.09 N. Find the volume of the wood.

Homework Statement Wikipedia tells me that I can obtain the surface area of a sphere by realizing that the volume of a sphere is equivalent to the infinite sum of the surface areas of hollow, nested spheres, sort of like little Russian dolls. That makes sense, and then differentiating both...

When doing constant volume calorimetry, the enthalpy can be calculated as follows: ΔH = ΔU + Δ(PV) ΔH = w + q + Δ(PV) ΔH = PΔV + q + Δ(PV) and at constant volume: ΔH = q + VΔP which I've then see people rewrite using the ideal gas law as follows: ΔH = q + (Δn)RT where Δn is the change in...

In 1-D the inverse of ∫ dx is dy/dx so how is the inverse of the volume integral ∫ d3x = ∫ dxdydz denoted ? Thanks

Hello guys, new member here. I've got a calculus project due Tuesday that I could use some help on. I won't bore you with the all details of the project, but first let's imagine an olive in the shape of a perfect sphere (with a radius always bigger than 6mm) that goes through a set of blades...

Homework Statement S is the sphere of equation x2 + y2 + z2 = 10z and C the cone of equation z= sqrt(3*( x2 + y2)) . The axes are measured centimeters. R of sphere = 5 D = 10 Total height is 10 cm Illustrate the solid E bounded by the C cone and the sphere S and calculate its volume using the...

Homework Statement : A cylinder is elongated by 2% of its original length. If Poisson's ratio of its material is 0.3. Calculate the percentage variation in volume.[/B]Homework Equations V = πr^2l η= 0.3= Δl/l/Δr/r[/B]The Attempt at a Solution I tried using calculus to differentiate V to find...

Hello, I'm in the process of creating a calculation spreadsheet with Excel. In this spreadsheet I need to calculate a volume of an object that has an arbitrary cross-section but from the side of the cross-section, it is always triangle. At the moment the spreadsheet calculates the volume of a...

Homework Statement I have the following task: Homework EquationsThe Attempt at a Solution But I don't understand how to solve it. Can somebody help me?[/B]

Hello, I work for a propane company where i unload propane rail cars. I am trying to figure out how much propane is being shipped back to the refinery after I off load the rail car. We are experiencing a large amount of shink and the accountant want to get to the bottom of it. With propane...

Homework Statement A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep. Homework EquationsThe Attempt at a Solution...

Homework Statement All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is (a) 1 centimeter and (b) 10 centimeters? Homework EquationsThe Attempt at a Solution I used the equation for the volume of a cube: V = s3 but I'm not...

Homework Statement At a processing plant, olive oil of density 875 kg/m3 flows in a horizontal section of hose that constricts from a diameter of 2.92 cm to a diameter of 1.20 cm. Assume steady, ideal flow. What is the volume flow rate if the change in pressure between the two sections of hose...

Homework Statement In a gas pipeline a mixture of hydrogen in air is transported. Usually, the hydrogen content of the gas is 1 volume %. It is well below the lower explosive limit as a hydrogen / air mixture is 4 % by volume hydrogen. gas pipeline is positioned a detector that activates an...

Homework Statement I have been tasked with designing a feasible experiment to determine the ration between 2 vessels. I think i have a way that works on paper. Homework Equations pV = nRT and the conservation of mass. The Attempt at a Solution 1.Start with 2 vessels of unknown volume x and y...

Homework Statement use spherical coordinates to find the volume of the solid inside the hemisphere z= √(25-x^2-y^2) and bounded laterally by the cylinder x^2+y^2=4 Homework Equations x=rcosθ =ρsinφcosθ , y=rsinθ =ρsinφsinθ z=ρcosφ r= ρsinφ The Attempt at a Solution I divided the solid into 2...

Do black hole singularities have 0 volume? What forces are keeping the particles from being in the same place?

So I'm getting ready for an exam on tuesday, and I'm using each method for volumes of revolutions for every problem but I'm not getting the same answers. So, let's use this as an example: y = 5x; the shaded region is from [1,2] Using the disk method (about the x-axis) I find: R(x) = 5x; r(x)...

Homework Statement Show that the internal energy at constant entropy and volume decrease for a spontaneous process Homework Equations F = U-TS The Attempt at a Solution Use Clausius: dS-dQ/dT > 0 Assume constant volume: TdS > dU assume constant entropy this becomes 0>dU Since dU is...

Homework Statement Find the volume of the solid bounded by z=x^2+y^2 and z=8-x^2-y^2 Homework Equations use double integral dydx the textbook divided the volume into 4 parts, The Attempt at a Solution [/B] f(x)= 8-x^2-y^2-(x^2+y^2)= 4-x^2-y^2 i use wolfram and got 8 pi, the correct...

If I, say, half the volume of a[n ideal] gas adiabatically, how on Earth can I tell how much the pressure will increase and how much the temperature will increase? PV=nRT Also, by what mechanism does the temperature increase? What would convince the molecules to move any faster? I can see why...

Homework Statement set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations y = 4 - x^2 z= 4 - x^2 first octant The Attempt at a Solution I am fairly confident in my ability to evaluate double integrals , but I am having a problem figuring...

Homework Statement Basically, this is part C of a question where in part A we had to use the RHS of the divergence theorem below to calculate the LHS, and then in part B we had to calculate the divergene of F, which came to be 0. and part C asks us how can this be? Since in part A we used the...

Homework Statement Compute the volume of the solid bounded by the four surfaces x+z=1,x+z=−1,z=1−y2,z=y2−1 Homework Equations Fubini's theorem? The Attempt at a Solution I have tried to visualize this solid and define the limits; when I attempted to integrate by dxdzdy (in that order), I set...