Cube-shaped 5916

Eric cleans up after playing with a cube-shaped cube with an edge of 14 cm. He cleans them into three boxes.
How many cubes can fit in:
1) cuboid with edges 4.2 dm, 5.6 dm, and 7dm?
2) a cube with an edge of 560 mm?
3) cuboid with edges 0.98m, 2.8 dm, and 42 cm?

Correct answer:

n₁ =  60
n₂ =  64
n₃ =  42

Step-by-step explanation:

$$\begin{gathered} a=14\text{cm} \\ V=a^3=14^3=2744{\text{cm}}^3 \\ {V}_1=42\cdot 56\cdot 70=164640{\text{cm}}^3 \\ {n}_1=V_1/V=164640/2744=60 \end{gathered}$$

$$\begin{gathered} a_2=560/10=56\text{cm} \\ {V}_2=a_2^3=56^3=175616{\text{cm}}^3 \\ {n}_2=V_2/V=175616/2744=64 \end{gathered}$$

$$\begin{gathered} V_3=98\cdot 28\cdot 42=115248{\text{cm}}^3 \\ {n}_3=V_3/V=115248/2744=42 \end{gathered}$$

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