Let

L = length of cuboid A, W = width of cuboid A, H = height of cuboid A

L = (1/2)L_{b} = (1/3) L_{c}

W = (2/3)W_{b} = (3/2) W_{c}

H = H_{b} = 3H_{c}

The dimensions of cuboids A, B, and C in terms of L, W and H are as follows:

(1) Cuboid A: L, W and H

(2) Cubiod B: 2L, (3/2)W and H

(3) Cuboid C: 3L, (2/3)W_{ }and (1/3)H

First, ratio for the volume:

V_{a} = LWH

V_{b}=2L•(3/2)W•H =3LWH

V_{c}=3L•(2/3)W•(1/3)H =(2/3)LWH

The ratio of the Volume is

A:B:C=1:3:2/3 = 3:9:2

Let’s think it this way, 2X2X2 cube and 3X3X3 cube has a side ratio of 2:3, a surface area ratio of 4:9 and volume ratio of 8:27. The pattern is square the side ratio to get the surface area ratio, then cube the side ratio to get the volume ratio. Therefore if you want to get the ratio of the surface area from the volume ratio, simply raise every number by 2/3 (same as get the cube root and then square it)

SA_{a}:SA_{b}:SA_{c}

3^{2/3}:9^{2/3}:2^{2/3}

=**9**^{1/3}**:81**^{1/3}**:4**^{1/3}

Krugen K.

Thank you very much.13d