The volumes of two similar solids are the the proportion of the cubes of

corresponding linear measures (sides in this case).

The lateral areas of two similar solids are the the proportion of the squares of

corresponding linear measures (sides in this case).

l1^3:l2^3 = 27:64

and we want:

l1^2:l2^2 = 27^{2/3}:64^{2/3} = 9:16

Therefor if the smaller lateral area is 18, the larger is (18/9)*16 = 32

RonL