Answer
1.3*10^-4
Work Step by Step
Aa initial volume is Vo of the liquid is cAo
Where
Ao= is the initial cross-section area
ho= 0.64
Final volume is V= hA
Where h is h - ho
Area = π r^2
dA=2π r dr= 2π r r α dT= 2α (π r^2 )dT= 2α AdT
The height is
h= V/A = Vο/Aο (( 1+ β(liquid) ΔT))/((1+2α(glass) ΔT))
Thus Vο/Aο = ho we obtain
h - ho = ho (( 1+ β(liquid) ΔT))/((1+2α(glass) ΔT -1))
=(0.64) (1 + (4*10^ -5) (10^0) / ( 1 + 2 (o 1*10 ^-5) (10^0)
=1.3*10^-4 is answer
