Volume Definition and 1000 Threads

Hi, I'm having quite a bit of trouble finding the propagation of uncertainty (using partial derivatives) of the volume of a hollow cylinder. The examples in my tutorial only demonstrates how to find the propagation of uncertainty on simple operations such as x + y, x/y, etc... 1. Homework...

New here, hope someone can help. I'm experimenting with a heat source for a steam turbine. I have the specs for the turbine and the necessary conditions for operation, but at this point in my design I need to figure out the volume of the actual boiler/reservoir. A direct answer or the right...

Hey guys. So I've been trying to learn Double Integrals on my own and I'm at Volume between surfaces...so googling some worksheet problems I came across the one and I'm a bit confused. 1. Homework Statement Let U be the solid above z = 0, below z = 4 − y^2, and between the surfaces x = siny...

Homework Statement How large a surface area in units of square feet will 1 gallon of paint cover if we apply a coat of paint that is 0.1cm thick? Homework Equations Since Volume is L * W * H and we can assume the object is square besides the height which in this case will be the thickness. So...

So I need to compare the results of the volume formula of a cylinder to the results of the integration. In geometry, you learn that the volume of a cylinder is given by V = πr2h, where r is the radius and h is the height of the cylinder. Use integration in cylindrical coordinates to confirm the...

Hello, I'm very new to physics & I've been stuck on this question, which seems pretty straight forward, for so long that I had to ask you guys :(. - d, (the diameter of the hole) is 0.184 cm - D (the diameter of the cylinder) is 0.916 cm - h (the height of the hole) is 2.33 cm - H (the height...

I've gone through many posts but haven't really come across something very clear. And on top of it my knowledge of fluid dynamics only extends to compressible fluids. I have a Nitrogen Cylinder Tank, with an exit pressure of 214.7 psia which is blocked by a solenoid valve at a location very...

In a trasformation in which P=costant, but internal pressure is different from external pressure, ΔH=Q? I'm asking this question because I know that Q=ΔU+PΔV (where P is the external pressure) and H=U+PV (where P is the sistem pression, so the internal pressure) Am I right?

Homework Statement I came across this equation denoting the work done by an open system (e.g. turbine or compressor). I wonder how they arrived at such an equation. Homework Equations Differential form of the steady flow energy equation for an infinitesimally small control volume neglecting...

Volume vs Circumference of a massive body. In the spacetime diagrams it is often shown that the space around massive bodies is warped in a way that seems to indicate the actual volume of a massive body is larger than 4/3 pi r^3. If you measure the radius from the circumference by traversing it...

Hello there, I've just been learning about surface magnetization currents circulating around hypothetical square loops. Since the magnetization is uniform the circulation currents cancel where the square loops are adjacent to one another and it can therefore be said that the current circulates...

it is given that the perimeter of the rectangle is (80 + 120 + 80 + 120) = 400 cm From this you need to make a cylinder with maximin volume: 400 = 2r + 2h 2h = 400 - 2r h = 200 - r . We wish to MAXIMIZE the total VOLUME of the resulting CYLINDER V = πr^2 h However, before we differentiate the...

My question is that I have to find the dimensions of a rectangular prism (cuboid), where none of the faces are square that will maximise its volume. The sheet metal I have to build it from is 120 cm by 80 cm. I don't even know where to start, I can do it if I'm given a height, width or length...

Hey guys! So the below question might sound like a homework question but in reality it is an oversimplified explanation of what I'm trying to measure Let's say we have a perfect machine that pushes out 600CFM into a box. On the other end of the box is another small machine that only consumes...

Is it possible to find the volume of a sphere(i know the formula) using definite integration ? And if possible how to proceed ?? Thanks in advance

Homework Statement Homework Equations V= Pi R2H The Attempt at a Solution V = Pi r2h They gave us the radius and the height (the length can be used as height). They Diameter is 0.9 to find the radius I just divide by 2 = 0.45. So now I find the volume of the cylinder using the formula “V=...

Homework Statement Homework Equations V= a21/3 h The Attempt at a Solution I may be wrong or right I don't know. I'm pretty sure I did it right.

Find the volume of the solid generated by revolving the region enclosed by y= cos x and y = -cos x for [-pi/2, pi/2] about the line y=2pi.

Please solve this problem :)

Hello. I am having some trouble with a work related problem. I have a GLP tank of 5000 litres capacity, and we actually have a pressure gauge on it measuring that the gas pressure on top of the liquid is above tolerance. Based only on that data, we need to measure the volume that is being taken...

Homework Statement You have been employed but(sic) the Mathematics Football League (MFL) to design a football. Using the volume of revolution technique, your football design must have a capacity of 5L ± 100mL. You must present a statement considering the brief below. Just a quick side note, I...

I am trying to gain some understanding from this article regarding deriving the volume of an arbitrary pyramid. "An arbitrary pyramid has a single cross-sectional shape whose lengths scale linearly with height. Therefore, the area of a cross section scales quadratically with height, decreasing...

Homework Statement A cylindrical glass tube (linear thermal expansion coefficient ##\alpha##) contains liquid (volume thermal expansion coefficient ##\beta##). The height of the tube is ##h_{t,0}## and the height of the liquid inside of it is ##h_{l,0}##. If the temperature changes of an amount...

The rate of working of the Reynolds Stress can be written as: where ui is the fluctuating velocity and Ūi is the time-averaged velocity. It is stated in the textbook that, if we integrate the above equation over a closed volume V, the divergence term on the left integrates to zero since τRij...

Homework Statement An ideal gass is at constant volume risen to a new pressure level of ##P_f##. Find te expression for the total heat brought to the system. Homework Equations 3. The Attempt at a Solution [/B] So ##PV=nRT## and ##E=Q## ##Q=C_v(T_f-T_i)## so i just have to find...

I read in http://www-library.desy.de/preparch/books/vstatmp_engl.pdf page 29 (43 for pdf) that the mean volume is: <V> = \int_{-\infty}^\infty dr V(r) N(r| r_0,s) I have two questions. Q1: why do they take the radius to be from -infinity to +infinity and not from 0 to infinity? Q2: is there an...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. (Use disk method) $$ xy = 3, y = 1, y = 4, x = 5 $$ Homework Equations [/B] The formula using for disk method is of the form: $$ \pi \int...

An allowed state of a molecule in a gas that is in a box of length L can be represented by a point in 3 dimensional K-space, and these points are uniformly distributed.In each direction points are separated by a distance π/L. A single point in K-space occupies a volume (π/L)^3. The number of...

Homework Statement For some gas specific heats for constant pressure and constant volume are calculated. Universal gas constant is R. Find the formula the helps identify the gas. Include only constants and given information. Homework Equations 3. The Attempt at a Solution [/B] Molar specific...

Let $U$ be a compact set in $\mathbb{R}^k$ and let $f:U\to\mathbb{R}^n$ be a $C^1$ bijection. Consider the manifold $M=f(U)$. Its volume distortion is defined as $G=det(DftDf).$ If $n=1$, one can deduce that $G=1+|\nabla f|^2$. What happens for $n>1$? Can one bound from below this $G$? If...

Hello! I am trying to crack the following problem: What is the pH of a solution formed by mixing 125.0 mL of 0.0250 M HCl with 75.0 mL of 0.0500 M NaOH? Here is how I am approaching the issue: both HCl and NaOH are strong acid and base respectively. Hence the concentration of [H3O+] =...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

I was just curious... what is the practical reason behind having two separate units for measuring volume? For instance, we can use cubic centimeters and mL interchangeably in practical medicine, i.e. injections. But we tend to use cubic (centi)meters for solids, and liters for liquids/gasses...

Homework Statement Find the volumes of the solid formed when each of the areas in the following perform one revolution about the X axis... Question: The volume line in the first quadrant and bounded by the curve y=x^3 and the line y=3x+2. Homework Equations Volume of revolution about X-axis...

Homework Statement The total area between a straight line and the parabola is revolved around the y-axis. What is the volume of revolution? According to the book, the answer is ; My answer comes out to be Homework Equations The Attempt at a Solution 1. Rewrite the second equation in...

Homework Statement Homework EquationsThe Attempt at a Solution Consider a very thin shell of width dr at a distance r from the center . The volume of this shell is ##4 \pi r^2 ## . Mass is ## m = 4 \pi r^2 \rho## . P is the pressure at distance r . Gravitational acceleration at distance r <...

I've always thought of dxat the end of an integral as a "full stop" or something to tell me what variable I'm integrating with respect to. I looked up the derivation of the formula for volume of a sphere, and here, dx is taken as an infinitesimally small change which is multiplied by the area of...

To start with, we should find the points of intersection of the two functions, as these will be the terminals of our regions of integration. $\displaystyle \begin{align*} 2\,x^2 &= x + 1 \\ 2\,x^2 - x - 1 &= 0 \\ 2\,x^2 - 2\,x + x - 1 &= 0 \\ 2\,x\,\left( x - 1 \right) + 1 \,\left( x - 1...

Here is a graph of the region to be rotated. Notice that it is being rotated around the same line that is the lower boundary. The volume will be exactly the same if everything is moved down by 4 units, with the advantage of being rotated around the x-axis. So using the rule for finding the...

Homework Statement Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 4 - x2 y = 0 Homework EquationsThe Attempt at a Solution Okay I understand that the region is symmetric about the y-axis...

I have water draining from a tank A into a tank B through a hole (or short pipe) and then being pumped back from B to A. If I know the rate of the pump (say 19 liters per minute), what should the diameter of the hole be so that the volume of tank A remains the same? The actual volume of A is...

The region between y = x & y = -x² + 2x revolves around y = x. Determine the volume.

Homework Statement Homework Equations Volume for cylinder = Pi (r)2 h Optimise : 1. make the best or most effective use of (a situation, opportunity, or resource). 2. rearrange or rewrite (data, software, etc.) to improve efficiency of retrieval or processing. The Attempt...

Homework Statement A slab of material has parallel faces. One coincides with the xy plane (z = 0), while the other is given by z = zt . The material has a nonuniform polarization P = P(1 + αz)zˆ where P and α are constants. Fin the volume and surface densities of bound charges[/B] The Attempt...

Homework Statement Use spherical coordinates to find the volume of the solid enclosed between the spheres $$x^2+y^2+z^2=4$$ and $$x^2+y^2+z^2=4z$$ Homework Equations $$z=\rho cos\phi$$ $$\rho^2=x^2+y^2+z^2$$ $$dxdydz = \rho^2sin\phi d\rho d\phi d\theta$$ The Attempt at a Solution The first...

A friend and I have been debating a topic for the last few days and I would really like a more informed opinion on the discussion. My friend says that IF you could, some how, see the universe from the outside and it appears that the universe is a finite flat, spherical shape, or other shape...

Homework Statement Hydrogen peroxide breaks down easily to give water and oxygen as follows: 2H2O2(aq)----> 2H2O2(l) + O2(g) Bottles of hydrogen peroxide are sometimes labelled as 10 volume as well as 3%. This means the volume of oxygen that can be liberated is 10 times the volume of the...

http://mathhelpboards.com/attachment.php?attachmentid=5579&stc=1 W9.3.8 Let $S$ be the region of the xy-plane bounded above by the curve $x^{3} y = 64$ below by the line $y = 1$, on the left by the line $x = 2$, and on the right by the line $x = 4$. Find the volume of the solid obtained by...

Homework Statement To a 25ml H2O2 solution, excess acidified solution of potassium iodide is added. The libereated iodine required 20ml of 0.3N sodium thiosulphate solution. Calculate the volume strength of H2O2. Homework Equations Normality = n-factor × Molarity Volume strength = Molarity ×...

Homework Statement I know that for constant volume ∂q=du and so du=Cv.dT However i don't understand how did we get to ∂q=du by neglecting the vdP term of enthalpy What I am trying to say is, is enthalpy this ∆U+P∂V+V∂P or this ∆U+P∂V? I don't understand since the definition of enthalpy is...