Thermal Expansion: Solve Problem w/Turpentine & Al Cylinder

[Sheneron]

Homework Statement

A hollow aluminum cylinder 18.0 cm deep has an internal capacity of 2.000 L at 24.0°C. It is completely filled with turpentine and then slowly warmed to 88.0°C. Note: If applicable, Table 19.1 is available for use in solving this problem.

The Attempt at a Solution

I solved part A and got an answer.

I can't figure out what I am doing wrong for part B, maybe someone can help.

When the cylinder heated up it expanded, as did the turpentine; the turpentine expanded more and then overflowed. So the remaining turpentine is the volume of the cylinder at 88C. So here is what I have set up.

Ok, it will take me a while to get the math in here, so maybe someone can just tell me if my concept is wrong and then that will be easy.

I know the volume of turpentine is the volume of the cylinder at 80C. So, with that, I can refind the volume of turpentine at 24C. Once I have the volume of the turpentine at 24C then I can set that to pi r^2 h, and solve for h. I can get r from initial conditions I was given. What is wrong with this thought process?

 

[Sheneron]

If I need to put the math tell me and I will do it.

 

[Sheneron]

Ohhhhhhhh nothing is wrong with that thought process is it? Thats right, someone tell me that right.