Volume with spherical coordinates

[aronclark1017]

Homework Statement

Volume above cone a=pi/3
Below sphere p=4 cosa

Relevant Equations

why 0<=a<=pi/2 not working?

I believe that I recall only have to use a part of the polar integral using cylindrical system

 

[haushofer]

Maybe I'm a bit dumb, but you have to be a bit more specific if you want to receive help. Personally I can't make anything out of this. If you want people to help you, put effort in a clear opening post.

 

[aronclark1017]

It must be because the pointer is spiraling upward as theta increases when using spherical coordinates. However using cylindrical coordinates it's simply using z. I will have to check z values as theta increases when I get a chance. Will also find the example using cylindrical coordinates. Someone must have a 3d animations program. I currently am in the process of drawing only 2d animation.

 

[FactChecker]

You may need to start at the beginning and describe the problem better. I have no clue what you are talking about.
What is $a$? $a=\pi/3$ is not a cone; it is a single value: $a=3.14159265358979/3 = 1.0471975511966$.
What is $p$? $p=4 \cos(a)$ is not a sphere; it is a single value: $p=2$.
What "pointer"? "Spiraling"??
What are you talking about?

 

[aronclark1017]

You may need to start at the beginning and describe the problem better. I have no clue what you are talking about.
What is $a$? $a=\pi/3$ is not a cone; it is a single value: $a=3.14159265358979/3 = 1.0471975511966$.
What is $p$? $p=4 \cos(a)$ is not a sphere; it is a single value: $p=2$.
What "pointer"? "Spiraling"??
What are you talking about?

a is my reference to the angle off the z axis. This is a cone shape for pi/3 for any angle t in the xy plane. The sphere is p=4cosa similarly where p is the spherical pointer and a is the angle off of the z axis.

 

[FactChecker]

I still don't know what you are talking about. A diagram might help. If you have a question, please don't feed us information a little at a time.

a is my reference to the angle off the z axis. This is a cone shape for pi/3 for any angle t in the xy plane.

Where does 't' come into this?

The sphere is p=4cosa similarly where p is the spherical pointer and a is the angle off of the z axis.

If $a=\pi/3$, then $p=4\cos(\pi/3)=2$. These are constants. They are not cones or spheres. How are you using them to define cones and spheres? You need to show some equations and, maybe, diagrams.

 

[aronclark1017]

Oh yeah is centered at 0,0,2 so is 2pi for the cone. Here z is dependent on p which appears to require 2 traces of the circle within the xy plane to get to the top of the sphere like it's spiraling upward as theta increases to 2 pi. Although in this cylindrical example #14 only one trace is needed I'm confused. I think is because although z is in terms of r , r reaches its max length with in one trace of the cylinder within the xy plane. Now the question is that if this also can apply to spherical coordinates such as if the former sphere were centered at 1,0,0. I'm not sure is confusing this feng. Even to me expert is trust is master of integrals.

 

[aronclark1017]

Correct me if I'm wrong...
if the sphere is p=sina, centered at 1/2,0,0 then only need theta between -pi/2, pi/2 because is nothing that exists in quadrant 2 and 3 and a for 0, pi/2 . but in the case that the sphere is centered at 0,0,1/2 p=cosa is theta for 0, 2pi and a for 0, pi/2.
this apply to both cylindrical and spherical system with polar equation just have to be spacially careful it seems. I just made a mistake in the where the sphere is centered and panicked.in my confusion.

-pseudo notes by one guy himself all by himself

 

[aronclark1017]

I'm just unclear on exactly what that pointer is doing need to plot many points or see some type of animator what matter any feng else really if no understand these concepts

 

[PhDeezNutz]

You made the effort to post what I presume is the answer guide. Can you post a picture of the actual question?

You talk about a cone at first and the picture shows a cylinder.

I’m with many others. Confused.

 

[PhDeezNutz]

I noticed your supposed solution paper is from 15.8 of Stewart’s calculus book.

Is it something like this?

 

[aronclark1017]

Yes is Stewart 5e calculus section cylindrical and spherical volume is expert of integrals. Justis at the point trying to understand what exactly the pointer is doing. In cases of polar equation on single plane where multiple trace with interval 0, 2pi what exactly the pointer is doing must know. Perhaps only way is to build paint application for 3 dimenions in .net windows form is also expert. But is very busy with documentation methods for larger scale projects and trying to find gym to battle bunyun seizures fro math strain stress.

 

[vela]

You may need to start at the beginning and describe the problem better. I have no clue what you are talking about.
What is $a$? $a=\pi/3$ is not a cone; it is a single value: $a=3.14159265358979/3 = 1.0471975511966$.
What is $p$? $p=4 \cos(a)$ is not a sphere; it is a single value: $p=2$.

I'm pretty sure the OP means the surface in R³ defined by $\theta = \pi/3$ in spherical coordinates, which is a cone, and the sphere given by $\rho = 4 \cos\theta$. The problem is to find the volume bounded by the cone on the bottom and the spherical cap on top.

 

[PeterDonis]

The OP question has been addressed. Thread closed.