Surface of cubes

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

Correct answer:

p =  1:4

Step-by-step explanation:

$$\begin{gathered} V=2\cdot 4\cdot 9=72{\text{cm}}^3 \\ {V}_1=\frac{1}{1+8}\cdot V=\frac{1}{1+8}\cdot 72=8{\text{cm}}^3 \\ {V}_2=\frac{8}{1+8}\cdot V=\frac{8}{1+8}\cdot 72=64{\text{cm}}^3 \\ {a}_1=\sqrt[3]{V_1}=\sqrt[3]{8}=2\text{cm} \\ {a}_2=\sqrt[3]{V_2}=\sqrt[3]{64}=4\text{cm} \\ {S}_1=6\cdot a_1^2=6\cdot 2^2=24\text{cm} \\ {S}_2=6\cdot a_2^2=6\cdot 4^2=96\text{cm} \\ p=S_1/S_2=24/96=\frac{1}{4}=0.25=1:4 \end{gathered}$$

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