Tagged Questions
3
votes
0answers
56 views
Calculating the Solid Angle
I've done some steps in this problem, but I got stuck at certain point.
$\textbf{Problem:}$ Consider we have a class $C^1$ parameterization ...
2
votes
1answer
69 views
tricky surface integral
I am studying for my final and my prof gave us review questions but with no answers so I am lost with this question. If anyone can help I would really appreciate it.
Question: Find the area of the ...
0
votes
2answers
76 views
Find surface area that lies above a triangle
Determine the area of the part of the surface $z=2 + 7x + 3y^2$ that lies above the triangle with vertices $(0,0)$, $(0,8)$, and $(14,8)$.
I do not know what formula to use to attempt this problem!
0
votes
1answer
34 views
Surface area of a plane inside a cone
Determine the surface area of the part of the plane $z=1+x+2y$ which is inside the cone surface $z=\sqrt{2x^{2}+10y^{2}}$.
1
vote
1answer
71 views
Stokes theorem problem to find alpha and beta so that I is independent of the choice of S
I have a question that I got half through but can't finish it. If anyone could help I would appreciate it.
Question: let C1 be the straight line from (-1,0,0) to (1,0,0) and C2 the semi circle ...
0
votes
0answers
52 views
Find area of a curvilinear triangle that includes hyperbolic functions
We were given this question in class and I tried to compute it and it looks to e pretty crazy. Can anyone take a look and let me know if I did it correctly... I would really appreciate it.
...
1
vote
2answers
88 views
Find area of a simple, smooth, closed curve lying in a plane
I was given this question in class and I assume it is a spin off of Green's theorem for finding the area of a closed curve $\lambda$ in 2D but expanded to 3D I believe. Anyways I am pretty confused ...
1
vote
2answers
37 views
How can we parametrize the following surface?
How to parametrize the following surface in $\mathbb{R}^3$: the intersection of $S=\{(x,y,z)\in\mathbb{R}^3:x^2+y^2+z^2\leqslant 1\}$ and $D=\{(x,y,z)\in\mathbb{R}^3:x+y=1\}$.
Any hints are ...
1
vote
1answer
49 views
Compute the surface area of an oblate paraboloid
Consider the surface S: $z=4-4x^2-y^2, z\geq0$. Compute its surface area.
I've tried the following: $Area(S)=\int\int_D \sqrt{(8x)^2+(2y)^2+1}dxdy$ with D being the interior of the ellipse ...
0
votes
0answers
73 views
Area of a surface sphere between two parallel planes
I am given the following question:
Consider the surface of a sphere (that is the boundary of the sphere) of radius $R>0$ in $\mathbb{R}^3$ and two parallel planes which are $R$ units away from ...
0
votes
1answer
54 views
Finding The Contour Maps Of A Function Of Two Variables
I am given the function $f(x,y) = \ln|y-x^2|$, and am suppose to find the contour maps.
Let $z = c = f(x,y)$. $c = \ln|y-x^2| \rightarrow e^c = e^{\ln|y-x^2|} \rightarrow e^c = |y-x^2|$
I know I ...
2
votes
0answers
103 views
calculating the area on the surface os a sphere created by intersection of two spherical caps!
Consider a spherical object composed of two compartments (A and B, not necessarily hemispheres) sitting at the interface which is characterized by a plane separating 1 and 2. For this case, ...
0
votes
1answer
141 views
What is the difference between surface area and scalar surface integrals?
What is the difference between the surface area of a paremetrized surface and the scalar surface integral of a function in $\mathbb{R}^3$? Are they not the same thing?
0
votes
1answer
70 views
Surface integral
Without getting into the whole question, I was asked to evaluate a surface integral
$\iint\limits_S f(x,y,z) da$
where S is the cylinder $x^2 + y^2 = x$
between $z=a$ and $z=b$
Now normally I ...
5
votes
0answers
72 views
surface of a torus by integration [duplicate]
Possible Duplicate:
surface area of torus of revolution
Let $R>r>0$ fixed. I want to compute the Area of $S=\operatorname{Im} \phi$ given by $$\phi(s,t):= \begin{pmatrix}(R+r\cos s ...
1
vote
3answers
136 views
Would this not take a ridiculously long calculation? (Surface area of parametric surface)
One of the question in my homework asks to verify that the surface are of
$ \mathbf{r} = a(1+\cos\phi)\sin\phi \cos\theta \mathbf{i} + a(1+\cos\phi)\sin\phi \sin\theta \mathbf{j} + ...
2
votes
0answers
72 views
How to determine whether or not a specified set is a smooth surface?
I know that a given set $M$ is a smooth surface of dimension $k$ in $\mathbb{R}^n$ iff there's a map $r:U\rightarrow\mathbb{R}^n, U\subset \mathbb{R}^k$ is open such that $\forall a\in U, ...
11
votes
3answers
713 views
Interesting implicit surfaces in $\mathbb{R}^3$
I have just written a small program in C++ and OpenGl to plot implicit surfaces in $\mathbb{R}^3$ for a Graphical Computing class and now I'm in need of more interesting surfaces to implement!
Some ...
