Surface area Definition and 451 Threads

Greetings, I'm trying to find the surface area of the part of the sphere x^{2}+y^{2} + z^{2}=1 above the cone z=\sqrt{x^{2}+y^{2}}. I know, that a surface area of a surface r(u,v) = x(u,v) + y(u,v) + z(u,v) can be given by, A(S) = \int\int | r_{u} \times r_{v} | dA A function, z=f(x,y) can...

A silo has cylindrical wall, a flat circular floor, and a hemispherical top. If the cost of construction per square foot is twice as great for the hemispherical top as for the walls and the floor, find the ratio of the total height to the diameter of the base that minimizes the total cost of...

i need MAJOR HELP! this is the problem: The can do tin can company minimizes costs by construckting cans from the least possible amount of material. this company suppplies many different sizes of cans to packing firms. a designer with the company needs to determine the radius that gives...

Homework Statement The curve is rotated about the y axis, find the area of the resulting surface. y=(1/4)X2-.5ln|x| 1<_X<_2 Homework Equations S=2(pi)(f(x))\sqrt{}1+f'(x)^2 The Attempt at a Solution Alright I'm not entirely sure where to even begin. Since I'm rotating about the Y-axis I know...

Two vessels of the same volume, in the same location and open to the atmosphere. One is tall and of a small diameter, the other is short and is of a larger diameter. Each vessel supplied with an identical heat source. Each vessel filled with an equal volume of an identical liquid. The goal...

Homework Statement A charge distributed uniformly over 1 face of the circular disk, find the surface charge density ? well i know density for surface charge is S= charge/area, the area for face of 1 circular disk is what ? 2pir ?

I have a problem that I've been stuck on for a while as follows, Find the surface area of the part of the cylinder x^{2}+y^{2}=2ay in the first octant that lies inside the sphere x^{2}+y^{2}+z^{2}=4a^{2}. Express your answer in terms of a single integral in \phi, you do not need to evaluate...

Homework Statement I have this function, and I need to find the Surface area of the function that is confined between the plains x=0, y=0 and z=0. My question is, what's D? Homework Equations The Attempt at a Solution

Homework Statement Find the area of the surface with parametric equations x=uv, y=u+v, z=u-v. u^2 + v^2 <= 1Homework Equations A(S)= double integral over the domain D of the norm of the cross product (r_u X r_v) DAThe Attempt at a Solution I started off with finding the norm of the cross...

Homework Statement I need help on an optimization problem involving a hexagonal prism with no bottom or top, but the top is covered by a trihedral pyramid which has a displacement, x, such that the surface area of the object is at a minimum for a given volume. The assigned variables include...

Homework Statement Find the area of the sphere x^2 + y^2 + (z-2)^2 = 4 that lies inside paraboloid z = x^2 + y^2Homework Equations The Attempt at a Solution when i take the equation of the spere and replace x^2 + y^2 with z i get: z(z-3) = 0 so they intersect at the plane z = 3. were supposed...

I have a question on the formulas for arc length and surface area. Do you use the formula: s= \int_{c}^{d}\sqrt{1+[g'(y)]^2}dy only when you are provided with a function x=g(y)?? Can you convert that to y=g(x) and solve it by replacing g'(y) with y(x), changing the bounds and the dy to dx...

I have a very faint idea of General Relativity.. hence this question. I think that according to General Relativity, the shortest distance between two points on this Earth is along a curved path, which is the curvature of the Earth [or sorta.. parallel to it]. Hence, i assumed that when on earth...

ok why does surface area = ( y) ( 1+ f ' (x)^(2) )^(1/2) equal surface area = (x ) (1+ f ' (x)^(2) )^(1/2) the simplest explanation please.

I was just thinking: If \iint dS is the surface area of a level surface, S, and \iiint dV is the volume of an enclosed solid, V, shouldn't \int df be the arclength of a function f(x)? Lets say that our surface is given implicitly by \Phi For the surface area we get: \iint dS =...

Homework Statement The question is to derive the surface area of a cone. Homework Equations slant= square root ( r^2 + h^2) surface area= int int [square root(fx^2 + fy^2 +1) da] surface area of cone side= pi *r(r^2+h^2) 3d cone formula: z= h/r(squareroot x^2+y^2) The Attempt at...

Homework Statement Express the surface area of a cube as a function of its volume. Homework Equations Cubic Volume=Length x Width x Height (V=Length of side^3) Cubic Surface Area= (Length of side^2)x6 The Attempt at a Solution f(V)=(X^3/X) x 6...sorry, I don't know if I'm on the...

Hello, the problem I'm working on is to find and set up the integral whose value is the area of the surface obtained by rotating the curve about the x-axis, then another integral to find the surface area by rotating about the y-axis. I do not need to evaluate these integrals, just set them up...

I just have a question, when I am rotating something let's say around y=2 and the two equations are x=t^3 + 1 and y = 4t+1 how would i set it up?

Find the area of the surface obtained by rotating the curve y=2e^(2y) from y=0 to y=4 about the y-axis. Any help on this would be greatly appreciated. This has my whole hall stumped. We know that you have to use the equation 2pi*int(g(y)sqrt(1+(derivative of function)^2), but cannot figure...

[SOLVED] Mobius Strip we have a normal strip of paper with surface area=A. if we make a mobius strip with it what will be the area of the mobius strip? is it A or 2A?

Homework Statement Find the area of the surface. The surface z = (2/3)(x^(3/2) + y^(3/2)), 0 </= x </= 1, 0 </= y </= 1 Homework Equations Double integral over S of the magnitude of dr/du cross dr/dv dS, which equals the double integral over D of the magnitude of dr/du cross dr/dv...

[SOLVED] Minimizing Surface Area Homework Statement A can is to be manufactured in the shape of a circular cylinder with volume = 50. Find the dimensions of a can that would minimize the amount of material needed to make the can. Homework Equations V = \pi r^2 h SA = 2 \pi r^2 + 2...

The Volume of a revolved function can be given by the integral of pi*f(x)^2*dx. For the arc length of a graph, a different integral is available. I understood the proof of these two and their integration is understandable. From such, I was actually expecting that the surface area of...

[SOLVED] Minimizing the Surface Area Homework Statement A box has a bottom with one edge 8 times as long as the other. If the box has no top and the volume is fixed at V, what dimensions minimize the surface area? Homework Equations V = lwh SA (with no top) = lw + 2lh + 2wh The...

Homework Statement A curce,C, has equation y=x^{\frac{1}{2}}-\frac{1}{3}x^{\frac{3}{2}}+\lambda where \lambda>0 and 0\leq x \leq 3 The length of C is denoted by s. Show that s=2\sqrt{3} The area of the surface generated when C is rotated through one revolution about the x-axis is denoted...

Homework Statement Find the surface area obtained when the upper half of the ellipse: \frac{x^{2}}{4}+ y^{2}=1 is rotated about the x-axis Homework Equations \int2piyds The Attempt at a Solution

Dear all, I was reading through my notes and I was kinda like stumbled in the way the minimum surface area of a cylinder has been derived. First, A= 2*PI*r^2 + 2*PI*r*h and given the condition that the volume has been fixed, the resulting area equation becomes A= 2*PI*r^2 + 2V/r...

Why a magnetic flux in closed surface area is always 0?

The given surface area of a sphere is 4*(pi)*r^2. There are several proofs to this, but I'm just looking for the error in this one: For the arc length, s = rx, x being the angle in radians. Therefore, s = 2(pi)r = C, C being circumference of circle. The surface are of a sphere is the sum...

[SOLVED] Surface Area Homework Statement Find the area of the surface of the part of the plane x + 2y + z = 4 that lies inside of the cylinder x^{2} + y^{2}=4 Homework Equations A(S)= \int\int_{D} \sqrt{1+( \frac{\partial z}{\partial x})^{2} + +( \frac{\partial z}{\partial y})^{2}}...

Hi, what do you think is the best method to determine/calculate in a computationally efficient way the solvent accessible surface area in phenomena like protein folding or protein-ligand docking ? Thanks

[SOLVED] Surface area of a sphere-derivation This isn't really a homework question, it just would've been handy to be able to do for an electromagnetism problem last year, and has been bugging me since! Is it possible to derive the surface area of a sphere by double integration? At the time I...

Am I correct in saying the surface parameterized by r = (sin v, u, cos v), v = [-pi/2, pi/2], u = [-1, 1] has an area of 2pi ? I get something different by computing the arc length of the parabola within the bounds and multiplying by 2. Which method is wrong?

Homework Statement For the homogeneous ice-cream cone that is given in spherical coordinates by rho= pi/4 (the bottom part) and phi=cos(rho) (the top part), find the volume, the center of mass, and the surface area. ((You have to do this problem using integrals, known formulas from...

Homework Statement The volume of a right circular cone is V = [(pie)(r^2)(h)]/3 and it ssurface area is S = (pie)(r)(r^2+h^2)^(1/2), where r is the base radius and h is the height of the cone. Find the dimensions of the cone with surface area 1 and maximum volume. The Attempt at a Solution...

Homework Statement (Q) Find the area of the surface cut from the paraboloid x^2+y+z^2 = 2 by the plane y=0. Homework Equations The Attempt at a Solution The unit normal vector in this case will be j. Moreover, the gradient vector will be sqrt(4x^2+4z^2+1). And the denominator...

Homework Statement (Q) Find the area of the portion of the surface x^2 - 2z = 0 that lies above the triangle bounded by the lines x = sqrt(3), y = 0, and y = x in the xy-plane. Homework Equations The Attempt at a Solution The know how to find the gradient vector. The part...

Hello I have a spherical triangle with the radius 1, and I have tried so hard to find the surface area. I know that A=120°, b=90° and c=60°. I could calculate that B=73.89° and C=56.31° and a=115.66°. I think I should use the formula (ABC) = (A + B + C - pi) r2 I always get the...

Here is some information I have for throttle bodys: 60 millimeters is equal to 2.362205 inches = 17.52 square inches 65 millimeters is equal to 2.559055 inches = 20.56 square inches - (17%) 70 millimeters is equal to 2.755906 inches = 23.85 square inches - (36%) 75 millimeters is equal to...

I need to find the surface area of z=x^{2}+2y where 0\leqx\leq1 and 0\leqy\leq1. I figured it's like trying any other surface area problem, but I think I'm misunderstanding how to set up this problem. Here is what I tried: \int^{1}_{0}\int^{1}_{0}\sqrt{2x+3}dydx = \frac{5\sqrt{5}}{3}-\sqrt{3}...

Homework Statement I have the following problem Assume that 30.0 cm^3 of gasoline is atomized into N spherical droplets, each with a radius of 2.00 x 10^-3 m. What is the total surface area of these N spherical droplets? Homework Equations SA = 4 * pi *r^2 V = 4/3 * pi * r^3The Attempt at a...

I have the following problem Assume that 30.0 cm^3 of gasoline is atomized into N spherical droplets, each with a radius of 2.00 x 10^-3 m. What is the total surface area of these N spherical droplets? I calculated the surface area of each atom to be 5x10^-9 m^2. I also calculated the volume...

A light year is the unit of distance that light, with a speed of 2.99792e8 m/s, travels in one year. What is the surface area of a planet whose radius is 1300 km? Answer in units of lightyears^2. I am wondering if my method is correct. SA of a sphere is 4[pi]R^2. With R = 1300, the...

How do we come to 4.pi.r^2?

Hi guys. Let's say we put a satellite on a geosynchronous orbit over the earth. The signal transmitted by the satellite does not reach the exact half of the Earth as much as you can intuitively try but is a portion formed by the two tangents from the point the satellite is on. The problem is to...

This is what i have so far SA = 2(pi)r^2 + 2(pi)r(245.45 / (pi)r^2) Derivative of SA = - 490.9r^2 + 4(pi)r 0 = -490.9r^2 + 4(pi)r and I'm stuck at this step.. I've tried a bunch of things to try and solve for r but i can't seam to get a logical answer for the radius of the minimized...

Homework Statement Find the blue colored surface area. 1 http://img338.imageshack.us/img338/1630/graph1zd7.png The radii of the circles are 3 cm and 1 cm. 2 Find the surface area of the rosette inside the equilateral triangle with side a. http://img87.imageshack.us/img87/2590/graph2dj9.png...

Homework Statement Find the surface area of the part of the cone z = sqrt[(x^2 + y^2)] lying inside the cylinder x^2 - 2x + y^2 = 0. 2. The attempt at a solution Partial Derivative x = x/sqrt(x^2 + y^2) Partial Derivative y = y/sqrt(x^2 + y^2) so... sqrt((Partial Derivative Y)...

Hi, I need some help on these problems. I'm not sure what to do. 1 Find the area of the plane with vector equation r(u, v) =< 1+v, u-2v, 3-5u+v> that is given by 0<u<1, 0<v<1. So far, I took the partial derivatives with respect to u and v. I don't know if I was supposed to or not and I'm...