Surface area Definition and 440 Threads

Could someone give a clue to how I could prove the sphere has minimal surface area for a given volume? Note this is not a homework problem. I saw in a chemistry textbook that water droplets tend to be spherical because each water molecule has a force directed inwards. In order to minimise the...

What is the most accurate way to estimate the surface area of a cylindrical bottle that decreases in diameter from its wides point (the body) to the narrowest point ( the neck and cap)? It seems like we did similar problems in calculus, however: 1. I don't remember any of it, and 2. I think...

Just had my test on Vector Fields and there was one question which really confused me. It asked to find the surface area of the parabaloid z = 9-x^2 -y^2 which is above the cone z = 8Sqrt[x^2 + y^2]. My memory told me to use the differential in rectangular coordinates and then convert to...

Here's the question: Find the area of the surface obtained by rotating the curve http://ada.math.uga.edu/webwork2_files/tmp/equations/18/d733a6e52ad8ca260230969bdc3f401.png from x=0 to x=9 about the x-axis. I'm supposed to parametrize the curve, using rcos(theta) as x and...

I've been looking at this method here: http://planetmath.org/encyclopedia/6668.html I was wondering at the last step before the "Note on multi-valuedness" if you wanted to obtain the general formula for the surface area of a sphere 4 \times \pi \times r^2 with a radius of well r what...

While doing electrolysis, Will the surface area of the node effect how much hydrogen is produced? Will it effect how well the current can pass through the water? Thank you

Find the surface area of the surface z=cosh(sqrt(x^2+y^2)) above the region in the xy plane given in polar coordinates: r is between 0 and theta theta is between 2 and 4 Ok. I used the formula: Surface area equals the square root of the partial derivative of x squared plus the partial...

May I have a tutor check over my question and solution? Problem Two rectangular sheets 20cm x 24cm and 15cm x 30cm are to be rolled to form cylinders. What is the height and diameter of the cylinder with maximum surface area that can be formed using either of these sheets? My Solution...

Find the surface area of the cone z=2sqrt(x^2+y^2) and above a region in the xy-plane with area 5. If anyone could help me with this problem, I would really appreciate it. Thanks. Mike

I am having trouble finding the surface area of a cube with the length of each edge equal to x+1. can some one help?

I'm attempting to solving this problem but do not know how to begin. Any help would be appreciate. What geometric surface encloses the maximum volume with the minimum surface area? How would you prove it?

Surface area integral sorry, this is not about flux integration... but surface area! sorry about the title! Find the surface area of the part of the sphere x^2+y^2+z^2=36 that lies above the cone z=\sqrt{x^2+y^2} z=\sqrt{36-x^2-y^2} A(S)=\int\int_D \sqrt{1+\left( \frac{\partial...

[FONT="Tahoma"] Can someone tell me how to find the surface area of a sphere when given the Area? :confused: thanks

Find the surface area when this curve is revolved around the x ax x = 1/3(y^2 + 2)^3/2 [1,2] I set it up both ways and i get two really complicated integrals. 2 \pi/3 \int_1^2 \sqrt{\frac{y^2+y^4}{(y^2+2)^{2/3}}} dy Yeah I can't figure out how to do this integral, and I am thinking there...

So, I've been reading Thornton and Marion's "Classical Dynamics of Particles and Systems" and have gotten to the chapter on the calculus of variations. In trying the end of chapter problems, I find I'm totally baffled by 6-9: given the volume of a cylinder, find the ratio of the height to the...

So, I had a question for all of you, regarding the relationships between area and circumference, and surface area and volume. For the longest time I was confused as to how these two quantities were related. I saw that the derivative of the area of a circle was equal to its volume, but then...

So the first thought that occurred to me was to use a surface integral I got 2pi*a^2, which is half the SA, if I used the surface integral is it possible or likely that I just found half the SA and can then multiply by 2? Or something. Actually, I think I see what I did, for my sec(gamma) I...

Can someone please help me with this question? x = 1-sint, y = 2+cost, rotate about y = 2 Find the surface area of the parametric curve. I don't know how to do it with y=2, I only know how if the question askes for rotating about the x-axis. The answer to the question is 2(pi)^2.

I was wondering what the surface area would be when the curve: x=e^tsint, and y=e^tcost where (t) is greater than or equal to (0) and (t) is less or equal to pi divided by (2). when it is revolved about a) the x-axis b) the y-axis (approximation...

Sphere 1 has surface area A1 and volume V1, and shere 2 has surface area A2 and volume V2. If the radius of shere 2 is four times the radius of shere 1, what is the ratio A2/A1 of the areas?

I want to find the surface area of only a part of the cylinder.what i mean is that the surface area that is under an angle theta in the cylinder.

Surface area help please... How do you find a surface area of a function around a vertical line? For example: surface of \ y=x^3 between \ 0<= x <= 3, rotating around \ x=4? I tried the formula for finding surface area, but I confuse with that vertical line x=4... what should I do?

Area/Volume Question Given the function on a 3D coordinate system: y = - z\sin \left( {xz} \right) where \left| {x - \frac{\pi } {2}} \right| \leqslant \frac{\pi }{z},\;z \ne 0 How do find the surface area of the figure integrated from z=a to z=b (where 'a' and 'b' are constants) ...

Howcome the ratio of the surface area of spheres are not equal to the ratio of volume of spheres? For example if I had two spheres, with an aspect ratio of 1:4 when comparing surface areas, yet I have 1:8 between those same spheres when comparing volume. This doesn't make sense to me...

So this question has been bothering me for a very long time... but only recently have I mustered up courage to register to ask it. Before though, let me draw a parallel analogy, so you can see where I'm coming from. When you take the volume of a region enclosed by one or more functions...

Hi, I have a question on the method of calculation of the surface area of a surface. I am using "Calculus Concepts and contexts by stewart", chapter 12.6. In it, he goes on to explain how to calculate the suface area of a surface as a double integral by using approximations. He breaks up...

Trying to figure out the answer to another thread. What is formula for the surface area of a dome? Googling got me 2\pi r h (where h is the height of the dome above its slice through the sphere). Is that right? Ultimately, I'm trying to figure out how the area changes as a function of...

Trying to figure out the answer to another thread. What is formula for the surface area of a dome? Googling got me 2\pi r^2 h

I have the following problem, which seems easy, I just cannot get my brain around it... Assume that 30.0 cm^3 of gasoline is atomized into N spherical droplets, each with a radius of 2.00\times 10^{-5} m. What is the total surface area of these N spherical droplets? How do I find the...

As part of a homework assignment, I am required to research Newton's Law of Cooling and evaluate it with three practical examples. One must be time of death. So far i have created a time of death example, and used an example to cool food. However the last one i heard someone say is that you...

ok I know how to solve for the volume no prob, but when you find the surface area, in all the proof they always drop the root, because something about being bigger than one Sqrt{1 + 1/x^4} dx can someone explain why they drop that, and how it's possible to have finite volume and infinite...

G'day all I'm new here this is my first post. I just found this forum in hope that you all can help me and I've hopfully come to the right place. i'm pretty bad at maths (actually shocking at it) and this may be a dumb question but any help would be appreciated. I'm doing total surface area...

find the surface area of f(x,y)=\sqrt{x^2+y^2} above the region R=\{(x,y):0\leq f(x,y) \leq 1\} well.. here's what the answer should be.. \sqrt{2} \ \theta 1. formula for Surface area: \int_{R} \int \sqrt{1+f_{x}(x,y)^2+f_{y}(x,y)^2} \ dA 2. next i need to find the region: so if...

i've been stuck on this problem for an hour now. how do you find the surface area for y=(x)^1/2 when 0_<x_<2, rotating about the x axis?

Can someone pull a rabbit out of a hat for me & explain why just because an object (like a cell or an animal) gets bigger, its surface area doesn't get proportionally bigger? I made myself a little chart where I took a sphere & found the vol & the s.a. at 1 cm radius, at 2 cm radius, and 3 cm...

I know that the equation for the surface area of any solid of revolution around, say, the x-axis is SA = 2\pi\int_{a}^{b} y\sqrt{1 + (\frac{\,dy}{\,dx})^2} \,dx What I need is the same formula except in parametric terms, like if the problem was given in terms of x(t) and y(t). Any takers?

I'm looking for a long list of trig equations. Mainly as of right now I'm looking for the equation to find the surface area of a sector of a sphere? Any help would be great, Thanks Philip

What's the difference b/w surface area and total area? For example, the surface area of a cylinder is A = 2 pi rh while the total area of a cylinder is A = 2 pi rh x 2 pi r^2. Thanks for the help =)

I think I'm on the verge of a breakthrough on this problem, but it's just not coming. Please tell me where my approach goes wrong or whether I'm correct but don't know how to integrate the resulting equation properly. The problem reads: A circular disk of radius r and thickness d is made...

Among all square-based pyramids which have volume V = 1, which one has the smallest surface area?