Discussion
The internal length, breadth and height of a cuboidal box are 12 cm, 10 cm and 8 cm, respectively. A cubical box has side (internal) 9 cm. Avin tries to pack 1800 cubical dice of side 1 cm each in these two boxes. The number of dice which are left unpacked is :
Answer: A
111 dice are left unpacked.
A 1 cm die occupies 1 cubic centimetre, and the internal dimensions are whole centimetres, so each box holds as many dice as its volume in cubic centimetres.
\[ \begin{aligned} \text{cuboid} &= 12 \times 10 \times 8 = 960 \\ \text{cube} &= 9 \times 9 \times 9 = 729 \\ \text{packed} &= 960 + 729 = 1689 \\ \text{unpacked} &= 1800 - 1689 = 111 \end{aligned} \]
The other options come from miscounting one of the two volumes; for example, \(9^{3}\) is often misremembered, so it is worth checking that \(81 \times 9 = 729\).
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