Solving for Volume Change: A Failed Attempt

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Homework Help Overview

The discussion revolves around a problem related to calculating the volume change of a geometric shape, specifically using the formula for the volume of a cone. Participants are attempting to analyze the relationship between the radius and height in the context of this volume change.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the volume formula v=1/3 pi r^2 h and explore the differentiation with respect to time. There is an attempt to substitute specific values for r and h, but some participants question the validity of these substitutions and suggest expressing r in terms of h instead. Others inquire about the relationship between r and h, considering trigonometric relationships.

Discussion Status

The discussion is ongoing, with participants providing feedback on the attempts made. Some guidance has been offered regarding the need to express r in terms of h, and there is an exploration of geometric relationships. Multiple interpretations of the problem are being considered, but no consensus has been reached yet.

Contextual Notes

Participants note constraints regarding the height h, indicating it should be less than or equal to 4. There is also a suggestion to reconsider the geometric setup based on a figure that is referenced but not provided in the discussion.

icystrike
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Homework Statement



attachment.php?attachmentid=25294&stc=1&d=1271861458.jpg


Homework Equations





The Attempt at a Solution



v=1/3 pi r^2 h
dv/dt = 1/3 pi (2rh dr/dt + r^2 dh/dt)
now i sub r=15/3 and h=3 .
Now i express dr/dt=dr/dh x dh/dt
and find dr/dh .
But it fails
 

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icystrike said:

The Attempt at a Solution



v=1/3 pi r^2 h
dv/dt = 1/3 pi (2rh dr/dt + r^2 dh/dt)
now i sub r=15/3 and h=3 .
Now i express dr/dt=dr/dh x dh/dt
and find dr/dh .
But it fails

The equation for v looks okay, as long as h is <= 4.

The substitution r = 15/3 is wrong.

You should be able to express r in terms of h. What is the relation between r and h? Note that if you use this, you can get just get rid of r altogether, which will be nice.

Cheers -- sylas
 
sylas said:
The equation for v looks okay, as long as h is <= 4.

The substitution r = 15/3 is wrong.

You should be able to express r in terms of h. What is the relation between r and h? Note that if you use this, you can get just get rid of r altogether, which will be nice.

Cheers -- sylas

could it be r=h tan (a) ? thanks btw =D
 
icystrike said:
could it be r=h tan (a) ? thanks btw =D

No.

Look again at the figure. Draw some water in it. Mark h and r for the given volume.
 

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