Volume of a solid limited by two paraboloids

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.
  • #1
aicort
6
0
Volume of a solid limited by these two paraboloids z=[tex]2x^2{}[/tex]+[tex]y^2{}[/tex] and z=12-[tex]x^2{}[/tex]-[tex]2y^2{}[/tex]



hi can someone help me? I tried to solve this and my solution was [tex]\ 24[/tex][tex]\Pi[/tex] is it correct? can someone solve this step by step?
 
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  • #2
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.
 
  • #3
aicort said:
Volume of a solid limited by these two paraboloids z=[tex]2x^2{}[/tex]+[tex]y^2{}[/tex] and z=12-[tex]x^2{}[/tex]-[tex]2y^2{}[/tex]



hi can someone help me? I tried to solve this and my solution was [tex]\ 24[/tex][tex]\Pi[/tex] 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.
 
  • #4
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
 
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  • #5
Looks good to me
 
  • #6
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.

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