100. The initial volume V

0

of the liquid is h

0

A

0

where A

0

is the initial cross-section area and h

0

= 0.64 m.

Its final volume is V = hA where h

− h

0

is what we wish to compute. Now, the area expands according

to how the glass expands, which is we analyze as follows.

A

=

πr

2

dA

=

2πr dr

dA

=

2πr (rα dT )

dA

=

2αA dT

Therefore, the height is

h =

V

A

=

V

0

(1 + β

liquid

∆T )

A

0

(1 + 2α

glass

∆T )

.

Thus, with V

0

/A

0

= h

0

we obtain

h

− h

0

=

h

0

1 + β

liquid

∆T

1 + 2α

glass

∆T

− 1



=

(0.64)



1 +



4

× 10

−5



(10

◦

)

1 + 2 (1

× 10

−5

) (10

◦

)



=

1.3

× 10

−4

m .