Surface area Definition and 440 Threads

Hey all, I was reviewing the concepts of how to derive the formula for the surface area, namely.. SA=\int \int \left\|\frac{\partial \widetilde{r}}{\partial u} \times \frac{\partial \widetilde{r}}{\partial v}\right\| dA (I didn't know how to make vector arrows so I used the tilde sign.)...

For r = 3, 0 < theta < pi/2, 0 < phi < pi/3, find the surface area of the sphere. The answer given is 9pi, but I can't seem to work it out. Below is my working: 2\int_{r=0}^{3}\int_{\phi=0}^{\frac{\pi}{3}}r\sin\theta dr d \phi + 2\int_{r=0}^{3}\int_{\theta=0}^{\frac{\pi}{2}}r dr d \theta +...

For r = 3, 0 < theta < pi/2, 0 < phi < pi/3 \int_{\theta=0}^{\frac{\pi}{2}}\int_{\phi=0}^{\frac{\pi}{3}}r^2sin\theta d \theta d \phi =R^2 [-cos\theta]_{0}^{\frac{\pi}{2}} [\phi]_{0}^{\frac{\pi}{3}} =(3^2)(1)(\frac{\pi}{3}) = 3\pi The above is my working. The answer should be the same as...

In calculus when you learn solids of revolution in relation to surface area or volume is there any specific uses that someone could enlighten me on in which this would be used. The only example I can think of is a lathe, and calculating its mass using the volume. Other then that I haven't seen...

Homework Statement Calculate the surface area of 1g of powder with a size of 100micrometer. Assume the particles are spherical. Then estimate the percentage of TiO2 molecules at the surface of the particle (relative to the total number of TiO2 molecules in the volume of the particle) for the...

Homework Statement I want to calculate the surface area, mapped with points. For starters, I've mapped the edge of a circle with 200 points, then created a few more circles, each with 200 points. The problem is I get different surface areas for the same size circles. The only difference...

Homework Statement Find the surface area generated by rotating y=5-4x^(3/2), 0\leq x\leq 1 about x=2.Homework Equations SA = 2\pi\int_{a}^{b}(r\cdot ds)dx The Attempt at a Solution I simply filled in the formula for the given question, and I'm getting stuck at integration time. SA =...

Homework Statement a)parametrize the upper surface of that portion of the sphere x^2 + y^2 +z^2 = 4 contained within the cylinder, x^2 + y^2 = 2y b)find the area of the surface Homework Equations how to find the range for phi. for paramaetrizing into spherical coordinates The...

Homework Statement How does the surface area of an object affect the force of static friction? I'm trying to figure out whether two different objects with equal mass and different surface areas requires the same amount of applied force or different amounts. Homework Equations I know of...

I have been thinking about the large number of "cold air intakes" and why they are such an overwhelming trend. I question their validity for a couple of reasons. First, the stock airbox on all new cars brings cold air in, usually from the fender, and is sealed off from the engine bay, usually...

Hello there. Suppose I have a function: y=3x^{2/3}-1 I want to find the surface area of the solid formed when the part of the curve between x=0 and x=8 is revolved about the x-axis.The curve crosses the x-axis at a point (1/3)^{3/2} The derivative of the function is...

Homework Statement Set up an integral that represents the area of the surface generated when the region is bounded by x + y2 = 1 and the y-axis, then rotated about the y-axis. All in one-variable. Homework Equations SA = 2pi \int xds possible x2 + y2 = r2 The Attempt at a Solution...

Homework Statement Find the area of the surface that is the boundary of the region enclosed by the surfaces x^{2}+y^{2}=9 and y+z=5 and z=0 Homework Equations A(S)=\int\int_{D}\left|r_{u}\times r_{v}\right| \; dA The Attempt at a Solution I am really confused as to what he...

Homework Statement A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. If building the tank covers $10 per square meter for the base and $5 per square meter for the sides, what...

not sure if my title is the most accurate but here is what I am asking. I will give general dimensions and weights in case it makes any difference. **EDIT** This is a pnuematic gun if you couldn't tell and if it makes any difference.** You have a hollow aluminum tube ~7/8" I.D. Inside the tube...

I have a generalised function in spherical polar co-ordinates that describes the radiant intensity in any given direction of a point source emitter. I need to calculate the fraction of the total radiation that is emitted into a region of space specified by some min to max range of elevation...

[Urgent] Surface area Homework Statement Hi there, sorry for the hurry, I had a big problem this weekend and I couldn't study. I have my exam tomorrow, and need help with this. I'm finishing with the topic, and I have almost studied all what I had to study, but this exercise resulted...

a cylinder has two identical cones one each end. the volume of the object is 50(pie/3) find the total height. so 2h+k=height. where to from there

I want to know how to increase the surface area of a liquid without doing any work. Heating would be counted in work done.

I can't get rearrange the last equation into a nice form to integrate with respect to x to minimize the surface area. http://i111.photobucket.com/albums/n149/camarolt4z28/2010-10-17122502.jpg?t=1287336976...

Homework Statement Near Earth, the density of protons in the solar wind (a stream of particles from the Sun) is 8.60 cm-3 and their speed is about 490 km/s. (a) Find the current density of these protons. 6.74E-7 A/m^2 (b) If Earth's magnetic field did not deflect the protons, what total...

Homework Statement Suppose a lipid droplet is essentially a sphere with a diameter of 1 cm. For A – D below, the area of a sphere is 4π r2, and volume is 4/3πr3. For π, use a value of 3.14. Show your calculations neatly in the space provided to receive credit for your answer. Round all...

Homework Statement Express the volume of a cube as a fuction of the total surface area Homework Equations Surface area = 6x^2 Volume = x^3 The Attempt at a Solution So, we need to manipulate the surface area equation so we can use it to find volume right? SA = 6x^2...

What is the pattern that maximizes the ratio of surface area of a flat surface to the volume of material used in this surface? The surface has to be flat on a macroscopic scale, but on the microscopic scale could have dimples or other imperfections that increase the SA/Volume ratio. I am...

volume and surface area of the sphere using integration ?? i was trying to find the surface area of the sphere using integration, ( by revolving circle on the x-axis ) the thing is it doesn't work as the volume problem. i mean in volume problem to get the volume of the sphere, you would...

Homework Statement i was trying to find the surface area of the sphere using integration, ( by revolving circle on the x-axis ) the thing is it doesn't work as the volume problem. i mean in volume problem to get the volume of the sphere, you would start with circle and start slice it...

Homework Statement Say the sphere of radius "a" is made out of various rings with height R(x) and thickness dx. Adding up all of the rings will form a sphere, and in order to do that, I have to integrate. Homework Equations Trigonometric Substitution: \frac{x}{a}=sin \theta dx=a cos...

Homework Statement Ok this is from a summer assignment that I had for calculus yet it's not calculus but it was graded by my calculus teacher so maybe there's something she knows that I don't from a calculus standpoint that allowed her to mark me wrong for this so here we go... Write a...

How do I express the surface area of for instance a sphere in terms of volume?

Homework Statement Find the surface area of a sphere whose volume is .2 m^3. For full credit, do it without finding the radius. Homework Equations This can be solved using v= 4/3(pi)r^3 and sa= 4(pi)r^2, but my prof doesn't want that. The Attempt at a Solution so if you...

Hi, I was just trying to find the surface area of a sphere without calculus, just for fun, but I ran into a little problem. The way I wanted to do it was by imagining a tennis ball, and cutting it in half forming a hemisphere. Then I imagined flattening out this hemisphere would preserve the...

1. Find the area of the surface generated by revolving y = (sqrt)(2x-x^2), x = [0,1] a. About the x axis b. About the y-axis This problem is from the section about surface area revolving around an axis. I actually did the problem but I am not sure on my answer. For around the...

Homework Statement Show that a black hole's event horizon will never shrink due to a Penrose process. Homework Equations M_{ir}^2 =\frac{1}{2}(M^2 + \sqrt{M^4-J^2}) The Attempt at a Solution It is easy to show that the irreducible mass will never decrease, and I know of a result that...

Homework Statement A regulation NCAA basketball is a sphere of radius approximately 12 cm. Grains of Texas beach sand are approximately spheres of radius 25 μm. If the inside volume of a basketball were completely filled with sand (assume perfect packing with no empty space) what is the...

Hi everyone, I've browsed around the forum a bit and found that others have had the same problem as me, however, none of the answers help me a lot, so I thought to post a more specific question, I hope you don't mind. I'm having a problem with the surface area of a sphere, probably because...

Homework Statement Find the surface area of that part of the plane 9x+10y+z=6 that lies inside the elliptic cylinder \frac{x^2}{25} +\frac{y^2}{100} =1 2. The attempt at a solution Once again I was just told that the surface area would be equal to the double integral of the area...

I currently have a question that i am struggling with it is: Propose a mathematical model in the form of an equation desribing, in general terms, the relationship between a given volume for a cylindrical container and the minimum surface area of material required to make it.. i am...

If 2 differently shaped objects are submerged in water, say one is rectangular and other spherical, and both displaces the same volume of water, would the surface area of both objects be the same?

Hi everyone! I'm new to online math forums. I wonder if anyone can give me a hand on this - it would be greatly appreciated. Thank you in advance! Dave Homework Statement If a box with a square base and an open top is to have a volume of 160 cubic feet, find the dimensions of the box having...

Homework Statement Consider the graph (see attachment) of r = 1 +2cos\Theta in polar coordinates. SET UP integrals to find 1. the area inside the large loop minus the area of the small loop. 2. the arc length of the small loop 3. the surface area of the surface formed by...

Homework Statement 1. Verify the given moments of inertia and find the center of mass. Assume each lamina has a density of p=1. The problem gives a circle with a radius a. 2. Find the area of the surface of the portion of the sphere x^2 + y^2 + z^2 = 25 inside the cylinder x^2 + y^2 = 9...

Homework Statement Find the surface area obtained by rotating the curve y = \frac{x^4}{16} + \frac{1}{2x^2} 1 < x < 2 about the y-axis. The attempt at a solution http://img341.imageshack.us/img341/3245/mathy.jpg My final answer is \frac{41\pi}{10}. Is this correct?

Homework Statement Homework Equations integral [a, b] 2*pi*x*sqrt(1 + (dy/dx)^2) The Attempt at a Solution Well I know how to do surface area questions... But that the @#$@ is with this random equation? How would I even start to evaluate it... Like honestly... I don't even understand the...

Homework Statement http://i47.tinypic.com/1z6naa.jpg Note... I used wolfram alpha to get the answer, I did not get it myself... So I still need help. The answer shown is correct, so you'll know if you got it. Homework Equations Integral [0, ln(4)] sqrt(1+(dy/dx)^2) The Attempt at...

Consider the region R bounded by f(x)=x^3, y =1, and x = 2. Find the surface area when f(x) is revolved around the line x=5. I know that the equation for surface area is the intergal from a to b of 2pi*r*h dx in all of the examples that I had done in class, everything was around the x or y...

Sorry I am new to the forum, I don't know how to type in the integrals and stuff. Homework Statement Let S be the portion of the surface y = x2 where 0 <= z <= X <= 2. Compute the surface area of S. Homework Equations r(u,v) = x(u,v)i + y(u,v)j + z(u,v)k A(S) = integral ru X rv dAThe Attempt...

Homework Statement Find the area of the surface obtained by rotating the curve y=1+5x2 from x=0 to x=8 about the y-axis Homework Equations As=\int2\pig(x)sqrt(1+[g'(x)]2) The Attempt at a Solution I changed the limits to suit the y direction, the lower limit becomes 1 and the...

Homework Statement A tungsten filament in a lamp is heated to a temperature of 2.30 x 10^3 K by an electric current. The tungsten has an emissivity of 0.31. What is the surface area of the filament if the lamp delivers 35.0 W of power? Homework Equations Stefan's Law (a greek letter...

My professor told me that the neutrons in a reactor see the surface area of nuclei, and not the the projected cross section. That really doesn't make intuitive sense. Is he right?

Homework Statement How do you solve the surface area of a sphere using Riemann Sums?Homework Equations The Attempt at a Solution I started out with 2 * (lim n->∞ [ (i=1 to n) ∑ [ 2*pi*(√(r^2 - (i/rn)^2))*(r/n) ] ]) where the summation is the surface area of the cylinders (or discs) inside a...