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 part made a cube. In what ratio are the surfaces of these cubes?

Result

p =  1:4

Solution:

$V = 2 \cdot \ 4 \cdot \ 9 = 72 \ cm^3 \ \\ V_{ 1 } = \dfrac{ 1 }{ 1+8 } \cdot \ V = \dfrac{ 1 }{ 1+8 } \cdot \ 72 = 8 \ cm^3 \ \\ V_{ 2 } = \dfrac{ 8 }{ 1+8 } \cdot \ V = \dfrac{ 8 }{ 1+8 } \cdot \ 72 = 64 \ cm^3 \ \\ \ \\ a_{ 1 } = \sqrt[3]{ V_{ 1 }} = \sqrt[3]{ 8 } = 2 \ cm \ \\ a_{ 2 } = \sqrt[3]{ V_{ 2 }} = \sqrt[3]{ 64 } = 4 \ cm \ \\ \ \\ S_{ 1 } = 6 \cdot \ a_{ 1 }^2 = 6 \cdot \ 2^2 = 24 \ cm \ \\ S_{ 2 } = 6 \cdot \ a_{ 2 }^2 = 6 \cdot \ 4^2 = 96 \ cm \ \\ p = S_{ 1 }/S_{ 2 } = 24/96 = \dfrac{ 1 }{ 4 } = 0.25 = 1:4$

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