Why Does Turpentine Not Overflow When Heated in an Aluminum Cylinder?

[Feodalherren]

Homework Statement

A hollow aluminum cylinder 2cm deep has an internal capacity of 2L at 20C. It is completely filled with turpentine and then slowly warmed to 80C.
a) How much turpentine overflows?
b)If the cylinder is then cooled back to 20 C how far below the cylinder's rim does the turpentine recede?

Homework Equations

Vnew=Vold(1+αΔT)^3

The Attempt at a Solution

I'm so confused. I just plugged and chugged into the formula.

It seems that the solutions manual uses the formula for the Al container, getting 2.0087L, which I follow. Then for the turpentine, they just do
2L(1+αΔT)=2.108L
So they do NOT cube it. What am I missing here? Why aren't they cubing the turpentine?

 

[Simon Bridge]

Did they use the volume or the linear expansion coefficient?

 

[Feodalherren]

Ahh they used linear for the Al and volume for the turpentine. Thanks a bunch!

 

[Chestermiller]

Ahh they used linear for the Al and volume for the turpentine. Thanks a bunch!

They should have cubed for both, unless the used the volumetric coefficient of expansion for aluminum.

Chet