Cubes

Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.

Result

S =  38880 cm2

Solution:

$n_{1}=135/12=\dfrac{ 45 }{ 4 }=11.25 \ \\ 12=2^2 \cdot 3 \ \\ 135=3^3 \cdot 5 \ \\ \text{GCD}(12, 12, 135)=3 \ \\ \ \\ a=GCD(12,12,135)=3 \ \\ V=12 \cdot \ 12 \cdot \ 135=19440 \ \\ n=V / a^3=19440 / 3^3=720 \ \\ S_{1}=6 \cdot \ a^2=6 \cdot \ 3^2=54 \ \\ S=n \cdot \ S_{1}=720 \cdot \ 54=38880 \ \text{cm}^2$

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