The volume of a box with a rectangular base is 3 072cm3.the length of the sides are in the ratio 1: 2: 3. calculate the length of the shortest side.

(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



Answers:

Length of the shortest side (X): 8 cm

Length of the side (Y): 16 cm

Length of the side (Z): 24 cm