Solving for Volume Change: A Failed Attempt

[icystrike]

Homework Statement

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

 

[sylas]

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

 

[icystrike]

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

 

[sylas]

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.