Surface of cubes

Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each piece made a cube. In what ratio are the surfaces of these cubes?

Correct result:

p =  1:4

Solution:

$$\begin{gathered} V=2\cdot 4\cdot 9=72{\text{cm}}^3 \\ {V}_1={\displaystyle \frac{1}{1+8}}\cdot V={\displaystyle \frac{1}{1+8}}\cdot 72=8{\text{cm}}^3 \\ {V}_2={\displaystyle \frac{8}{1+8}}\cdot V={\displaystyle \frac{8}{1+8}}\cdot 72=64{\text{cm}}^3 \\ {a}_1=\sqrt[3]{V_1}=\sqrt[3]{8}=2\text{ cm } \\ {a}_2=\sqrt[3]{V_2}=\sqrt[3]{64}=4\text{ cm } \\ {S}_1=6\cdot a_1^2=6\cdot 2^2=24\text{ cm } \\ {S}_2=6\cdot a_2^2=6\cdot 4^2=96\text{ cm } \\ p=S_1\mathrm{/}{S}_2=24\mathrm{/}96={\displaystyle \frac{1}{4}}=0.25=1:4 \end{gathered}$$

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