To find the volume of the box in terms of books, we first need to calculate the volume of the box and then compare it to the volume of one book.
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Calculate the volume of the box: The box is a rectangular prism with:
- 5 layers (height = 5 units)
- Each layer is 4 units long and 6 units wide.
Volume of the box \( V_{box} \) is calculated using the formula for the volume of a rectangular prism: \[ V_{box} = \text{length} \times \text{width} \times \text{height} = 4 \times 6 \times 5 \] \[ V_{box} = 120 \text{ cubic units} \]
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Calculate the volume of one book: The book itself is also a rectangular prism with:
- 1 layer (height = 1 unit)
- 2 units long
- 3 units wide.
Volume of the book \( V_{book} \) is calculated similarly: \[ V_{book} = \text{length} \times \text{width} \times \text{height} = 2 \times 3 \times 1 \] \[ V_{book} = 6 \text{ cubic units} \]
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Determine how many books fit in the box: To find the number of books that fit in the box, we divide the volume of the box by the volume of one book: \[ \text{Number of books} = \frac{V_{box}}{V_{book}} = \frac{120}{6} = 20 \]
Therefore, the volume of the box in terms of books is 20 books.