Volume of three cuboids

Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.

Correct result:

V =  1506 cm3

Solution:

x=6 a1=x=6 b1=2x=2⋅ 6=12 c1=3x=3⋅ 6=18 V1=a1⋅ b1⋅ c1=6⋅ 12⋅ 18=1296 a2=x/2=6/2=3 b2=x=6 c2=3⋅ x/2=3⋅ 6/2=9 V2=a2⋅ b2⋅ c2=3⋅ 6⋅ 9=162 a3=x/3=6/3=2 b3=2⋅ x/3=2⋅ 6/3=4 c3=x=6 V3=a3⋅ b3⋅ c3=2⋅ 4⋅ 6=48 V=V1+V2+V3=1296+162+48=1506 cm3

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