Discussion
The inside measurements of a card board is 1.5×0.75×0.60 m³. The number of books of dimension 20×10×7.5 cm³ that can be arranged in the box are
Answer: C
450 books can be arranged in the box.
Work in centimetres. The box is 150 cm by 75 cm by 60 cm, and each book is 20 cm by 10 cm by 7.5 cm.
\[ \begin{aligned} \text{box} &= 150 \times 75 \times 60 = 675000\ \text{cm}^{3} \\ \text{book} &= 20 \times 10 \times 7.5 = 1500\ \text{cm}^{3} \\ \text{number} &= \frac{675000}{1500} = 450 \end{aligned} \]
The books also pack the box exactly with nothing left over: stand the 7.5 cm side along the 75 cm edge (10 books), the 10 cm side along the 150 cm edge (15 books) and the 20 cm side along the 60 cm height (3 layers), and \(10 \times 15 \times 3 = 450\). 350, 400 and 500 do not fit either the volume or any arrangement.
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