Surface area Definition and 450 Threads

Homework Statement Find the surface area of the portion of the cylinder x^2+y^2=4y lying inside the sphere x^2+y^2+z^2=16Homework Equations Double integral for finding surface area. \iint_S d\sigma The Attempt at a Solution At first, i thought it was just the area of the surface of sphere...

Homework Statement A small sphere of mass m carries a charge of q. It hangs from a silk thread which makes an angle θ with a large charged non-conducting sheet. Calculate the surface charge density on the sheet. Homework Equations ∫E.ds The Attempt at a Solution I found E of...

Homework Statement Find the area of the surface z=7+2x+2y2 that lies above the triangle with vertices (0,0) (0,1) and (2,1) The Attempt at a Solution It's not a particularly difficult problem to set up, I just can't seem to get a simple integrand. ∫∫√(16y2+5) dA is what I come up...

Hello, I have a major in economics and I am creating an excel spreadsheet for quotations of sheet metal ductwork as my final thesis. I need to calculate weights for various types of ductwork produced in the company I chose for my thesis. In order to calculate weight, I need to know the...

Realm of the Mad God actually takes place on a spherical planet where Oryx's minions thrive. This planet has a mass of 2.73 x 10^24 kg and a gravitational acceleration of 11.2 m/s^2 at its surface. Roughly 840,000 minions live per square kilometer. Together, the players of the realm kill 1500...

Homework Statement Imagine you have a rectangular piece of cardboard measuring 3 feet by 4 feet. You know that if you cut a square out of each corner, you can fold the pieces together and tape them together to make an object that looks like a shoe...

why do paddles/oars have a large surface area? I thought that it does not really matter as i would just apply a force on the water so as to attain a action-reaction force on the boat thus pushing me forward. but if i look at the free body diagram of the paddle 1 force will be me pushing and the...

I'm researching solar cells, some of which use TiO2 as a semiconducting film. Modern solar cells use TiO2 nanoparticles to increase the surface area of the film. Somehow this is advantageous to the solar cell. From my limited understanding of semiconductors, I know that to get a current...

i have found the area of sphere in two ways using the same approximation.but i get two different answers ;one the correct value 4∏R^2?how does this happen? i'm attaching the solution below?please refer to the attachments and give a solution?

I need to find the total surface area of the hollowed out hemisphere (picture attached), with an inner diameter of 1.86 cm and what looks like an outer radius (also what I am assuming as height) of 1.25 cm. Surface area of a sphere is 4∏r2, so half the sphere is 2∏r2. Since the outer...

Homework Statement Find the surface area of a sphere of radius R that is illuminated by a light that is held h units away from its surface.Homework Equations integral surface area formula i don't know how to type it up properly on here. The Attempt at a Solution I have NO idea how to do this...

Homework Statement Find the area of the surface obtained from rotating the curve x = ln(y) - y^2/8 on [1,e] about the y-axis. Homework Equations SA = \int 2\pi*(f(x))*\sqrt{1+[f'(x)]^2}dx The Attempt at a Solution SA = \int 2\pi*(ln(y) - \frac{y^2}{8}))*\sqrt{1+\frac{9}{16*y^2}}dy from 1 to e...

Homework Statement Find surface area of solid of revolution obtained by rotating the curve: y=x2/40-5lnx from x=5 to x=7, rotated about x=-4 The Attempt at a Solution The problem is I know how to do this if I rotated it about x-axis/y-axis, but I have no idea how to do it if the...

i just need some help on how to start the process of proving it. suggestions/recommendations/anything will help!

got stuck on doing the substitution.. any suggestions?

Homework Statement For upper hemisphere S: x^2 + y^2 + z^2 = 1 , with z≥0, find the area element dS and unit normal vector N. Compute the total area of the hemisphere, ∫∫dS over S. Homework Equations Unit normal to surface f(x,y,z) = const N(hat) = grad(f)/|grad(f)| Surface area...

Homework Statement I understand everything except for the part where the -1 pops out of nowhere on step 4. why? how?

So I'm working on a chemistry lab determining Avogadro's constant with a fatty acid monolayer on a beaker of water, and my calculations are all work out to around 1.3*10^23 (ie a sixth of what they should be). The lab said "fill the beaker with water until it spills over". In doing so, I ended...

Homework Statement A boiler drum is equipped with hemispherical heads (i.e. the two heads together make a sphere.) The diameter of the drum is 0.8 meters and the drum is 5 meters in length. Calculate: a.) The area of insulation required to cover the entire drum. b.) The total...

Hello everyone, I recently tried to find the surface area of a hollow cone (there is no base, like an ice cream cone) using spherical coordinates. With cylindrical coordinates I was able to do this easily using the following integral: \int \int \frac{R}{h}z \sqrt{\frac{R^{2}}{h^{2}} + 1}...

Animal Brain size, body mass, and surface area S.J. Gould wrote a series of interesting articles (chapters 22-24 in Ever Since Darwin) about the ratio of body mass to brain mass among animal species. Bigger animals have bigger brains (of course) but the ratio is getting smaller: a human's brain...

Evaluate surface area of top hemisphere Homework Statement http://s1.ipicture.ru/uploads/20120106/jrHc5122.jpg The attempt at a solution This problem is new to me, in the sense that the integration is to be done against S, which is the same region S, over which the limits are defined...

Homework Statement This isn't actually a homework problem, but rather a class of problems I'm running into as I study for prelims. I'm taking these from Greenspan's Calculus: An Introduction to Applied Mathematics. This type of problem has come up in the context of both volume and surface...

Find the surface area of the triangle with vertices (0,0) (L, L) (L,-L) I know I have to take the double integrals of f(x,y) but I have no idea what f(x,y) is supposed to be!

Homework Statement The portion of the paraboloid 2z=x^2+y^2 that is inside the cylinder x^2+y^2=8 The Attempt at a Solution my attempt was that i would turn this into polar coordinates and solve that integral but is it right? I came up with...

I’m doing a lot of double integrals to find surface area problems, and I don’t think I’m setting them up quite right. For example, “Find the surface area of the portion of the sphere x^2 + y^2 + z^2 = 25 inside the cylinder x^2 + y^2 = 9.” I converted the sphere to a function of z: \sqrt{25...

Homework Statement I believe this is intended to be a proof of the formula πrl, surface area of a cone. Homework Equations A complete volume of revolution gives you a cone - the height h is the x value on a graph, the radius r is the y value. The y intercept is zero, therefore y=r/hx ...

Homework Statement Determine the surface area of the roof of the structure if it is formed by rotating the parabola about the axis. Homework Equations SA=\int _0^{16}{2\pi\left ( 4 \sqrt{16-y} \right ) dy} (?) The Attempt at a Solution SA=\left [ -\frac{16}{3}\pi\left ( 16-y...

Homework Statement The total surface area of a right circular cylinder is given by the formula A = 2pir(r + h) where r is the radius and h is the height. a) Find the rate of change of A with respect to h if r remains constant. b) Find the rate of change of A with respect to r if h remains...

Ok, so I have problems understanding where they came up with the formula S=2∏rL, where r = (1/2)(r1+r2). They say the formula is verified in exercise 62. I did the exercise and showed that S=∏rL. Correct me if I'm wrong, but isn't this contradictory? I can see how they're using the...

Homework Statement Find the surface area of the cone with the following equations: x= u sin(a)cos(v) , y= u sin(a)sin(v), z=u cos(a) where 0<=u <=b , 0<=v<=2(pi), a is constant! The Attempt at a Solution Trying to solve this I first calculate the absolute value of the cross product of r'(u)...

Actually I changed my mind and feel like it should be ((pi*r)(2*pi*r)) by my faulty thinking. Since pi*r would give you a line wrapped halfway around a sphere, I was thinking you could repeat this line in a radial pattern around the outside of a sphere (2*pi*r) times to get the surface area...

Homework Statement Is minimiznig the area of tin used to make a can an important factor? Suppose a manufacturer wishes to enclose a fixed volume,V, using a cylindrical can. The height of the cylinder is denoted by h, and the radius of the cylinder can section by r. i)Write a function for the...

Is there a general formula to measure the amount of heat lost per second (Joules per second) given the surface area which the water covers and the width of the insulator material surrounding it?

Hi all I was just wondering about the dependence of radiative transfer from a body, on its surface area and not the volume. As per stefan's law, the variation is (StefanConstant * SurfaceArea* Temp^4) The primary source of these electromagnetic radiation is from the charges in the body...

Hi there, I have to compute the surface area for V:\{ -2(x+y)\leq{}z\leq{}4-x^2-y^2 \} I have a problem on finding the surface area for the paraboloid limited by the plane. I've parametrized the plane in polar coordinates, I thought it would be easier this way, but also tried in cartesian...

Hello I've been stuck with this for ever, can't find the relevant formulas Homework Statement Given that the surface area of the first heat sink, S1= 500 cm2 = 0.05 m2 2nd heat sink = ? The thermal resistance between p-n junction and case, RTjb = 0.6˚C/W The thermal resistance...

solve this integral The area of a circle can be found by the washer method The exact area of a washer is dA = 2 \pi r \,\,dr \,\,\,\,\,\,\,eq.1 Area of a circle is: \int 2 \pi r \,\,dr Equation 1 mulitplied by h (height) gives the exact volume of a cylindrical shell: dV = 2 \pi r...

Homework Statement i am trying to apprixmate the surface area of a hemisphere. i am approximating by cutting the sphere into cylinders of different radius, and using their curved surface area to approximate. each cylinder will have a height of r.cos.theta and radius of r.sin.theta...

I'm trying to determine the contact surface area of a threaded bolt so that I can make some changes to the design and maintain the same contact surface so as not to affect the performace in other ways. This presents itself as a helix, and my initial guess was that it may be best to work this...

Find the surface area of that portion of the sphere x^2 + y^2 + z^2 = a^2 that is above xy-plane and within the cylinder x^2 + y^2 = b^2 , 0 < b < a Solution.. i try to find fx and fy.. http://imageshack.us/f/594/33049204.jpg/" how am i going to proceed?

My problem: I calculate, using Differential Geometry, the surface area of a specific part to be 50% more than the surface area AutoCAD calculates it to be using the AREA command on an extruded solid. I am certain that my calculations are correct. I use theorems of Differential Geometry that...

Homework Statement the filament of a light bulb has a temperature of 2580Cel. and radiates 60W of power. The emissivity of the filament is 0.36. What is the surface area of the filament? Homework Equations P= \sigma*A*emissivity*T^4 A=? \sigma=\sigma\ =\ 5.670400(40)\ \times\...

I am solving for the surface area of a helical ribbon that I represent as a ruled surface, the curve being the helix and the rulings being in the vertical \sigma\left(t,\varphi\right)=\left(\begin{array}{ccc} r\cos t, & r\sin t, & \omega t+\varphi\end{array}\right) I solve for the terms in...

Homework Statement Find the area of the part of the cylinder y^2+z^2=a^2 that lies inside the cylinder x^2 +y^2 = a^2 Homework Equations The Attempt at a Solution So the first thing I did was I solved for z from the first equation to get z = Sqrt[a^2-y^2]. I took the partial...

Homework Statement Find the area of the part of the surface z^2 = 2*x*y that lies above the xy plane and is bounded by the planes x=0, x=2 and y=0, y=1. Homework Equations The Attempt at a Solution z = Sqrt[2*x*y] Sqrt[(partial z/partial x)^2 + (partial z/partial y)^2 +1] =...

Homework Statement 4. The domain D is a tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1 Calculate (a) The volume of the domain. (b) The x-coordinate of the centre-of-mass of the domain, assuming constant density. (c) Find, in terms of x and y the vector R from the origin...

I was able to get an answer to this homework problem, but I have no way of verifying that it is correct. I was hoping someone more experienced than me could look over my work and let me know if I did the problem correctly. Homework Statement Find the surface area of the part of the...

Homework Statement The domain D is a tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1 Calculate (a). The volume of the domain. [10 marks] (b). The x-coordinate of the centre-of-mass of the domain, assuming constant density. [9 marks] (c). Find, in terms of x and y the...

Hi, I want to calculate the surface area of the Menger Sponge and found the following explanation online: N = number of square faces in the sponge) N[0] = 6 N[1] = 8N[0] + 4x6x1 (each face of original is split into 8, and also 4x6 for the holes) N[2] = 8N[1] + 4x6x20 (each face of N[1]...