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Help with finding the volume of a triangle using definite intergral

  • #1
Hi. I need some help for a test tomoorow on thi sone kind of problem:

Homework Statement


Set up and evaluate an intergral to find the olume of a cone of height 12 m and radius 3 m at teh open end.


A fast replay would be realy helpful.
 

Answers and Replies

  • #2
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Hi. I need some help for a test tomoorow on thi sone kind of problem:

Homework Statement


Set up and evaluate an intergral to find the olume of a cone of height 12 m and radius 3 m at teh open end.
What do you know about finding volumes of rotation? I would set up the integral (not intergral -- there is no such word) using disks.
 
  • #3


What do you know about finding volumes of rotation? I would set up the integral (not intergral -- there is no such word) using disks.
...um. I know how to do volumes or rotations, but this is a cone, not a line on a graph.
 
  • #4
He's talking about cross-sections I'm pretty sure...first what you want to do it find the height of your chunk, and then, using the standard formula for the geometric shape, set up the definite integral and evaluate it if necessary...
 
  • #5
He's talking about cross-sections I'm pretty sure...first what you want to do it find the height of your chunk, and then, using the standard formula for the geometric shape, set up the definite integral and evaluate it if necessary...
You're still not makin gmuh sence.
 
  • #6
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A cross section of your cone looks like an isosceles triangle whose height is 12m and whose base is 6m. If you rotate this triangle around the y-axis, you get a cone.

You can get the volume by using disks, where the radius of the disks decreases as you go from the bottom to the top.
 
  • #7
A cross section of your cone looks like an isosceles triangle whose height is 12m and whose base is 6m. If you rotate this triangle around the y-axis, you get a cone.

You can get the volume by using disks, where the radius of the disks decreases as you go from the bottom to the top.
I'm still not getting this. Can you work it out so I can see it?
 
  • #8
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No. Look in your textbook for an example. Per the rules of this forum, you need to make a good effort at solving the problems you post. So far I haven't seen any effort on your part.

Here's an excerpt from the rules (https://www.physicsforums.com/showthread.php?t=5374).
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.​
 
  • #9
No. Look in your textbook for an example. Per the rules of this forum, you need to make a good effort at solving the problems you post. So far I haven't seen any effort on your part.

Here's an excerpt from the rules (https://www.physicsforums.com/showthread.php?t=5374).
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.​
so..you want me to look in a textbook that dosen;t explain how it got it's answer.
 
  • #10
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5,191
Your textbook should have worked examples showing how to calculate volumes of revolution using both the disk method and the shell method. Every calculus text I've ever seen has numerous worked examples of each kind.
 
  • #11
Your textbook should have worked examples showing how to calculate volumes of revolution using both the disk method and the shell method.
My textbok doesn't really explain how to do it. It jsut does it.

And besides, I did try to do this problem for the last 45 minutes, and i got nowhere. Also, the books explaination in an exmple problem makes no sence....



EDIT: Figured it out, lock please.
 
Last edited:

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