Discussion
A 4080 cu.cm cubical room can contain how many maximum number of boxes having dimensions 4 cm, 3 cm and 2 cm?
Answer: A
Compare volumes, since the box dimensions divide the room's cleanly.
\[ V_{\text{box}} = 4 \times 3 \times 2 = 24 \text{ cm}^{3} \]
\[ n = \frac{4080}{24} = 170 \]
A volume division only gives an upper bound in general, because packing can waste space; here it is achievable, since 24 divides 4080 exactly and the boxes can be laid in aligned layers.
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