Cardboard box

Peter had a square piece of cardboard whose edge length was an integer number of decimetres. He cut a 3 dm square from each corner and folded up the sides to make a box that held exactly 108 unit cubes (each with a 1 dm edge).
Julia cut 2 dm squares from each corner of the same size cardboard and made a box. She wants to fill it with cubes that have a 2 dm edge. How many cubes will fit in Julia's box?

Final Answer:

n =  16

Step-by-step explanation:

$$\begin{gathered} V=108\cdot 1^3=108{\text{dm}}^3 \\ c=3\text{dm} \\ V=a^2\cdot c \\ a=\sqrt{V/c}=\sqrt{108/3}=6\text{dm} \\ x=a+2\cdot c=6+2\cdot 3=12\text{dm} \\ {c}_2=2\text{dm} \\ {a}_2=x-2\cdot c_2=12-2\cdot 2=8\text{dm} \\ {V}_2=a_2^2\cdot c_2=8^2\cdot 2=128{\text{dm}}^3 \\ {V}_3=2^3=8{\text{cm}}^3 \\ n=V_2/V_3=128/8=16 \end{gathered}$$

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