Finding the Volume of a Rotation About the x and y Axis

  • Context: Undergrad 
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    Axis Rotation Volume
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Discussion Overview

The discussion revolves around finding the volume of solids formed by rotating a specific curve, defined by the equation 2y² = x³, about the x-axis and y-axis. Participants explore the mathematical methods involved in calculating these volumes, including considerations for partial rotations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks help in calculating the volume of a solid formed by rotating the region bounded by the curve, the y-axis, and the line y=2 about the y-axis and then about the x-axis.
  • Another participant suggests that rotating about the x-axis can be approached by swapping x and y in the given relation and then applying the same method used for the y-axis rotation.
  • A participant expresses frustration with their attempt to rearrange the equation for the second rotation, indicating that their substitution did not yield the correct answer.
  • One participant advises that a more descriptive title could attract more responses, suggesting that the current title is too common.
  • A later reply humorously proposes a more eye-catching title for future posts to garner attention.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the methods for calculating the volumes, and there is uncertainty regarding the correct approach to the problem, particularly in the second part of the question.

Contextual Notes

There are indications of missing assumptions in the mathematical steps taken, particularly regarding the rearrangement of the equation for the second rotation. The discussion does not resolve these issues.

Habosh
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hi
this is my first post,and I hope i get the help I need;)
equation of curve 2y^2=x^3 find the volume of the solid formed by the complete rotation about the y-axis of the region bounded by the curve the y azis and the line with the equation y=2 which lies in the first quadrant,*done this*
npw i need help in second part of the question
find also the volume formed when the region is rotated completely about the x axis
I also have a question would anyone help me and explain what shall we do if the rotation was not 360 about the x axis,but was 180
thanx in advance:D
 
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Rotating about the x-axis is mathematically equivalent to swapping x and y in the relation given then rotating about the y-axis so that whatever method you used in the first problem should work for the second problem.

Also, rotating halfway will give you half the volume of a full rotation.
 
well that is what driving me crazy,because in the second one I tried to make the equation with the y as a subject then squared it and substituted with 2 but it didn't work the answer was wrong:(
 
suggestion: curiosity is more powerful an attraction than academic pity. try stating the problem next time in the title. your current title has been used a lot before, and to me personally is often reason enough to ignore the post.
 
hehe:Dok then i will next time i'll post a thread with the title I have a phsycic powers is a math fourm:p that will surely attract some attention
 

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