Solid with polar graph as base

In summary: There is no reason to think this is a cylinder until you have established (with words) that it is a cylinder. You cannot just assert it and expect anyone to help you.In summary, the conversation is about a video where the speaker is trying to understand the equation for the xy plane projection. The conversation includes discussions about the use of integrals and the relevance of the calculations done. The expert suggests that the speaker should explain their reasoning and use more words to clarify their working.
  • #1
fonseh
529
2

Homework Statement




In this video , why for the xy plane projection , it's a circle with center = y = 1 , i can understand the r = 2sin theta ? why we can't ∬ r dr dtheta where , r = 1 , and with theta = 0 to 2 pi ?

They are the same , right ? since volume = integration of area with z a-xis in this case...

Homework Equations

The Attempt at a Solution

 
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  • #2
In this video , why for the xy plane projection , it's a circle with center = y = 1
because geometry ... that is the projection of the region being integrated over.
The lecturer derives the equation on the board for you.

Where did he lose you?
 
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  • #3
Simon Bridge said:
because geometry ... that is the projection of the region being integrated over.
The lecturer derives the equation on the board for you.

Where did he lose you?
i did in in another way , but didnt get the ans ...

My ans is :
 

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  • #4
Sure ... but not relevant.
If you will not answer questions I cannot help you.

note: hardly anyone reads pictures - I'm cutting you lots of slack just watching the video.
I did look at the pic - it does not mean anything to me.

In order for a bunch of symbols to mean anything, you have to explain the reasoning you used for doing that in the first place. If you will not explain your reasoning, nobody can help you.

Have another go.
 
  • #5
Simon Bridge said:
Sure ... but not relevant.
If you will not answer questions I cannot help you.

note: hardly anyone reads pictures - I'm cutting you lots of slack just watching the video.
I did look at the pic - it does not mean anything to me.

In order for a bunch of symbols to mean anything, you have to explain the reasoning you used for doing that in the first place. If you will not explain your reasoning, nobody can help you.

Have another go.
which part you don't understand ?

In the pictures , i calculate the area first m then i integrate the area over the height , so for the working at the left hand side , it's the area , for the right hand side , it's the integration of area over the height
 
  • #6
fonseh said:
which part you don't understand ?

In the pictures , i calculate the area first m then i integrate the area over the height , so for the working at the left hand side , it's the area , for the right hand side , it's the integration of area over the height

How about typing out a clear statement of the problem? I, for one, will not look at the video; I figure that if you want help you will take the time to explain your problem. (BTW: I am by no means alone here; most helpers will not look at your submission, and you are just plain lucky to have found one who did.)
 
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  • #7
fonseh said:
which part you don't understand ?
pretty much all of it. I can see you did some integrals... all integrals are areas. I don't know which areas you are calculating or what for. OR how it is relevant. Don't get me wrong, they are nice integrals, pretty, look good on camera. Not everyone can take photos of a sheet of maths and have them come out so nice, but I have to be psychic to know what you intended them to do or why so I can have any way to evaluate whether what you did was at all valid, never mind correct.

When doing maths, also use words.

In the pictures , i calculate the area [of something not mentioned using a reasing you don't explain] first m [what is this "m"] then i integrate the area over the height [how do you integrate an area over a height?], so for the working at the left hand side [guessing "of the page"... don't make people guess what you mean], it's the area, for the right hand side , it's the integration of area over the height
... the words need to explain your reasoning too.

Start again from the top, annotate your working as you go... or just answer the question in post #2... then, maybe, some will be able to help.
 
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  • #8
Simon Bridge said:
pretty much all of it. I can see you did some integrals... all integrals are areas. I don't know which areas you are calculating or what for. OR how it is relevant. Don't get me wrong, they are nice integrals, pretty, look good on camera. Not everyone can take photos of a sheet of maths and have them come out so nice, but I have to be psychic to know what you intended them to do or why so I can have any way to evaluate whether what you did was at all valid, never mind correct.

When doing maths, also use words.

... the words need to explain your reasoning too.

Start again from the top, annotate your working as you go... or just answer the question in post #2... then, maybe, some will be able to help.
cant i just calculate the area first ? then i integrate the area of the base with the height to get volume , since this is a cylinder , so , the area of the 'circle ' is constant for every plane throughout the whole length ?

What i mean is imagine a a cylinder is made of many thin planes (circle)stacked together to form a solid cylinder .... So, i calculate the area of base first , then i only multiply with the quantity of the thin planes(circle) , which is the height here

So, area of thin planes (circle ) = pi(1^2) = pi , then integrate with the height , which if from z = 2y to z = (x^2) + (y^2) , is it wrong to do so ?
 
  • #9
fonseh said:
cant i just calculate the area first ?
Depends, which area?
... then i integrate the area of the base with the height to get volume , since this is a cylinder , so , the area of the 'circle ' is constant for every plane throughout the whole length ?
Are we looking at the same problem? vis: the volume to be calculated in post #1 is not a cylinder.

I'm sorry - you have consistently failed to answer questions or follow sugestions - I cannot help you.
Good luck.
 
  • #10
Simon Bridge said:
Depends, which area?
Are we looking at the same problem? vis: the volume to be calculated in post #1 is not a cylinder.

I'm sorry - you have consistently failed to answer questions or follow sugestions - I cannot help you.
Good luck.
sorry , here's the question



I'm sorry that i have posted the wrong question .
 
  • #11
fonseh said:
sorry , here's the question



I'm sorry that i have posted the wrong question .


You really do not want help, so you? You have been advised to NOT show the problem as a video or picture---just type it all out---but you have refused every time. Helpers will not bother to help you if you cannot even be bothered to type the problem. The choice is up to you.
 
  • #12
Ray Vickson said:
You really do not want help, so you? You have been advised to NOT show the problem as a video or picture---just type it all out---but you have refused every time. Helpers will not bother to help you if you cannot even be bothered to type the problem. The choice is up to you.
refer to the question here
https://www.physicsforums.com/threads/volume-of-cylinder.894188/#post-5625165
 

FAQ: Solid with polar graph as base

1. What is a solid with polar graph as base?

A solid with polar graph as base refers to a three-dimensional figure formed by rotating a polar graph around its central axis. The polar graph can be represented by a curve or a set of points in polar coordinates.

2. How is a solid with polar graph as base different from other solids?

The main difference is that a solid with polar graph as base has a curved surface, while other solids typically have flat surfaces. Additionally, the polar graph as base allows for more complex shapes to be formed, such as spirals and cones.

3. What are some real-life examples of solids with polar graph as base?

A common example is a cone, which can be formed by rotating a straight line (polar graph) around its central axis. Other examples include seashells, tornadoes, and the shape of some fruits and vegetables.

4. How do you calculate the volume of a solid with polar graph as base?

The volume of a solid with polar graph as base can be calculated using the formula V = ∫[a,b]πf(x)^2dx, where f(x) represents the polar curve and a and b represent the limits of integration. This formula is similar to the one used for calculating the volume of a solid of revolution.

5. Are there any practical applications of solids with polar graph as base?

Yes, there are many practical applications of these types of solids in fields such as engineering, architecture, and design. For example, cones and spirals are commonly used in construction and manufacturing, and the shape of certain fruits and vegetables can be optimized for packaging and transportation.

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