Volume of a solid limited by two paraboloids

• aicort
In summary, the conversation is about finding the volume of a solid limited by two paraboloids, with one person requesting help in solving the problem and showing their own solution. Another person then asks for clarification and offers assistance. The original person confirms their solution is correct and thanks them for the help.
aicort
Volume of a solid limited by these two paraboloids z=$$2x^2{}$$+$$y^2{}$$ and z=12-$$x^2{}$$-$$2y^2{}$$

hi can someone help me? I tried to solve this and my solution was $$\ 24$$$$\Pi$$ is it correct? can someone solve this step by step?

Last edited:
I am assuming you are in calculus. In this case you would find the intersection of these two functions, and integrate the difference of the two functions over the areas.

aicort said:
Volume of a solid limited by these two paraboloids z=$$2x^2{}$$+$$y^2{}$$ and z=12-$$x^2{}$$-$$2y^2{}$$

hi can someone help me? I tried to solve this and my solution was $$\ 24$$$$\Pi$$ is it correct? can someone solve this step by step?

How did you get your result of 24 pi? Show us what you did and we'll help you with it.

BTW, you should have posted this in the Calculus & Beyond section, not the Precalculus Math section.

Mark44 said:
How did you get your result of 24 pi? Show us what you did and we'll help you with it.

BTW, you should have posted this in the Calculus & Beyond section, not the Precalculus Math section.

yeah i know... i realized too late :P i hope someone move this thread to that section
look this is what i did

http://img413.imageshack.us/img413/2806/volt.th.jpg

Last edited by a moderator:
Looks good to me

you say so? I'm glad then... i thought it was wrong
thanks you guys :)

1. What is the formula for calculating the volume of a solid limited by two paraboloids?

The formula for calculating the volume of a solid limited by two paraboloids is V = ∫∫∫ dV = ∫∫∫ dxdydz.

2. How do I determine the bounds of integration for calculating the volume?

The bounds of integration can be determined by finding the points of intersection between the two paraboloids and setting up triple integrals for each region between the paraboloids.

3. Can the volume of a solid limited by two paraboloids be negative?

No, the volume of a solid limited by two paraboloids cannot be negative. It represents the amount of space enclosed by the two paraboloids and is always a positive value.

4. Are there any real-world applications of calculating the volume of a solid limited by two paraboloids?

Yes, this concept is commonly used in engineering and architecture to calculate the volume of objects such as water tanks, silos, and building structures.

5. Is there a specific method for calculating the volume of a solid limited by two paraboloids?

Yes, the most common method for calculating the volume of a solid limited by two paraboloids is by using triple integrals and setting up the appropriate bounds of integration.

• Precalculus Mathematics Homework Help
Replies
11
Views
843
• Precalculus Mathematics Homework Help
Replies
2
Views
556
• Calculus
Replies
2
Views
1K
• Precalculus Mathematics Homework Help
Replies
8
Views
396
• Precalculus Mathematics Homework Help
Replies
5
Views
744
• Precalculus Mathematics Homework Help
Replies
5
Views
794
• Precalculus Mathematics Homework Help
Replies
8
Views
1K
• Calculus
Replies
6
Views
2K
• Calculus
Replies
7
Views
2K
• Calculus
Replies
5
Views
1K
The text passage discusses a specific mathematical problem involving the calculation of the volume of a solid limited by two paraboloids. The original poster provides their solution and asks for verification, which is confirmed by another user.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Volume of a solid limited by two paraboloids

• aicort
In summary, the conversation is about finding the volume of a solid limited by two paraboloids, with one person requesting help in solving the problem and showing their own solution. Another person then asks for clarification and offers assistance. The original person confirms their solution is correct and thanks them for the help.
aicort
Volume of a solid limited by these two paraboloids z=$$2x^2{}$$+$$y^2{}$$ and z=12-$$x^2{}$$-$$2y^2{}$$

hi can someone help me? I tried to solve this and my solution was $$\ 24$$$$\Pi$$ is it correct? can someone solve this step by step?

Last edited:
I am assuming you are in calculus. In this case you would find the intersection of these two functions, and integrate the difference of the two functions over the areas.

aicort said:
Volume of a solid limited by these two paraboloids z=$$2x^2{}$$+$$y^2{}$$ and z=12-$$x^2{}$$-$$2y^2{}$$

hi can someone help me? I tried to solve this and my solution was $$\ 24$$$$\Pi$$ is it correct? can someone solve this step by step?

How did you get your result of 24 pi? Show us what you did and we'll help you with it.

BTW, you should have posted this in the Calculus & Beyond section, not the Precalculus Math section.

Mark44 said:
How did you get your result of 24 pi? Show us what you did and we'll help you with it.

BTW, you should have posted this in the Calculus & Beyond section, not the Precalculus Math section.

yeah i know... i realized too late :P i hope someone move this thread to that section
look this is what i did

http://img413.imageshack.us/img413/2806/volt.th.jpg

Last edited by a moderator:
Looks good to me

you say so? I'm glad then... i thought it was wrong
thanks you guys :)

1. What is the formula for calculating the volume of a solid limited by two paraboloids?

The formula for calculating the volume of a solid limited by two paraboloids is V = ∫∫∫ dV = ∫∫∫ dxdydz.

2. How do I determine the bounds of integration for calculating the volume?

The bounds of integration can be determined by finding the points of intersection between the two paraboloids and setting up triple integrals for each region between the paraboloids.

3. Can the volume of a solid limited by two paraboloids be negative?

No, the volume of a solid limited by two paraboloids cannot be negative. It represents the amount of space enclosed by the two paraboloids and is always a positive value.

4. Are there any real-world applications of calculating the volume of a solid limited by two paraboloids?

Yes, this concept is commonly used in engineering and architecture to calculate the volume of objects such as water tanks, silos, and building structures.

5. Is there a specific method for calculating the volume of a solid limited by two paraboloids?

Yes, the most common method for calculating the volume of a solid limited by two paraboloids is by using triple integrals and setting up the appropriate bounds of integration.

• Precalculus Mathematics Homework Help
Replies
11
Views
843
• Precalculus Mathematics Homework Help
Replies
2
Views
556
• Calculus
Replies
2
Views
1K
• Precalculus Mathematics Homework Help
Replies
8
Views
396
• Precalculus Mathematics Homework Help
Replies
5
Views
744
• Precalculus Mathematics Homework Help
Replies
5
Views
794
• Precalculus Mathematics Homework Help
Replies
8
Views
1K
• Calculus
Replies
6
Views
2K
• Calculus
Replies
7
Views
2K
• Calculus
Replies
5
Views
1K
user
The text passage discusses a specific mathematical problem involving the calculation of the volume of a solid limited by two paraboloids. The original poster provides their solution and asks for verification, which is confirmed by another user.

TYPE: SINGLE_QUESTION_WITH_ANSWER