Relating coefficients of volume, linear expansion with height

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Homework Statement


a liquid with a coefficient of volume expansion B(beta symbol) just fills a spherical shell of volume Vinitial, at a temp of Tinitial. The Shell has average coefficient of linear expansion a(alpha symbol). The liquid is free to expand into a open capillary of area A projecting from the top of the sphere. A) the temp increases by delta(change symbol)T. Show that the liquid rises in the capillary by the amount delta,h given by the equation delta,h=(Vintial/A)(B-3a)(deltaT).

-B is the beta coefficient Volume expansion(i dont know how to actually type that in)
-a is alpha linear explansion
-A is area

Homework Equations


changeofV=BVinitial(changeoftemp)
B=3*a(aplha)

The Attempt at a Solution


im kind of confused at how to do this problem since everything is given in variables and no actual quantitys are involved, i also dont have anything in my notes in regards of how to relate changeof height to change of volume but anyhow

my attempted solution, changeofh=(Vinitial/A)(B-3a)(Tinitial+changeofT).....
 

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