let the sides of the first box be
a, b , and c m
ab = 48 #1
ac = 96 #2
bc = 288 #3
divide #1 by #2 --> b/c = 1/2 or c = 2b
divide #2 by #3 --> a/b = 1/3 or b = 3a
divide #1 by #3 --> a/c = 1/6 or c = 6a
we know ab = 48
a(3a) = 48
3a^2 = 48
a^2 = 16
a = 4
then b = 12
and c = 24
the volume of the first box must be
4x12x24 or 1152 m^3
the second box must have each side as 4 m
so its volume is 4x4x4 = 64 m^3
so the ratio of theri volumes = 1152:64
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