Cubes into cuboid

How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8,4dm and 4,8?

Result

n =  140

Solution:

a1=12/10=65=1.2 dm V1=a13=1.23=216125=1.728 dm3  a=6 dm b=8.4 dm c=4.8 dm V2=a⋅ b⋅ c=6⋅ 8.4⋅ 4.8=604825=241.92 dm3  n=V2/V1=241.92/1.728=140a_{ 1 } = 12/10 = \dfrac{ 6 }{ 5 } = 1.2 \ dm \ \\ V_{ 1 } = a_{ 1 }^3 = 1.2^3 = \dfrac{ 216 }{ 125 } = 1.728 \ dm^3 \ \\ \ \\ a = 6 \ dm \ \\ b = 8.4 \ dm \ \\ c = 4.8 \ dm \ \\ V_{ 2 } = a \cdot \ b \cdot \ c = 6 \cdot \ 8.4 \cdot \ 4.8 = \dfrac{ 6048 }{ 25 } = 241.92 \ dm^3 \ \\ \ \\ n = V_{ 2 }/V_{ 1 } = 241.92/1.728 = 140

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