Solving for Volume Change: A Failed Attempt

Draw in the angle a, and label it. Now write down some simple trigonometry equations, using the information you have marked.Then solve these equations for r in terms of h.Once you have done this, use the formula for v and you should find it all works out.Cheers -- sylasIn summary, the conversation discusses finding the derivative of the volume of a cone with respect to time and solving for the rate of change of the radius. The initial attempt at solving the problem using a substitution for r is incorrect. The expert suggests expressing r in terms of h and using basic trigonometry to solve for it. This will lead to a correct solution for the problem.
  • #1
icystrike
445
1

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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  • #2
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
 
  • #3
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
 
  • #4
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.
 

What is volume change?

Volume change refers to the change in the amount of space occupied by a substance or object. It can be measured in units such as cubic meters or liters.

What is the importance of solving for volume change?

Solving for volume change is important in understanding the behavior and properties of substances and objects. It can also be used in various applications such as designing structures and conducting experiments.

What is the formula for calculating volume change?

The formula for calculating volume change is V = Vf - Vi, where V is the volume change, Vf is the final volume, and Vi is the initial volume.

What are some common reasons for a failed attempt at solving for volume change?

A failed attempt at solving for volume change could be due to incorrect measurements, using the wrong formula, or neglecting the effects of temperature and pressure on volume. Another reason could be experimental errors or limitations in equipment.

How can errors in solving for volume change be minimized?

To minimize errors in solving for volume change, it is important to use precise measurements and the correct formula. It is also important to account for any external factors, such as temperature and pressure, that may affect volume. Repeating experiments and using more accurate equipment can also help minimize errors.

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