(1) The volume of a box with a rectangular base is 3072 cm³...
X x Y x Z = 3072 cm³
(2) The length of the sides are in the ratio 1:2:3
This means that:
(X)*(2X)*(3X) = 3072 cm³
It also means that:
Y=2X
Z=3X
(3) Calculate the length of the shortest side...
(X)*(2X)*(3X) = 3072 cm³
6X³ = 3072 cm³
X³ = (3072 cm³)/6
X³ = 512 cm³
X = ∛(512 cm³)
X = 8 cm
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Answers:
Length of the shortest side (X): 8 cm
Length of the side (Y): 16 cm
Length of the side (Z): 24 cm