John has a storage bin in the shape of a rectangular prism. The storage bin measures 3 feet long, 2 feet wide, and 2 feet tall. John will put boxes that measure foot on each side into the bin. 2 f1 2 ft hat is the greatest number of boxes John can put into the bin?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Text:**

John has a storage bin in the shape of a rectangular prism. The storage bin measures \(3 \frac{1}{2}\) feet long, 2 feet wide, and 2 feet tall. John will put boxes that measure \(\frac{1}{2}\) foot on each side into the bin.

**Diagram Explanation:**

The diagram illustrates a rectangular prism representing John's storage bin. The dimensions of the bin are marked:

- Length: \(3 \frac{1}{2}\) feet
- Width: 2 feet
- Height: 2 feet

Inside the bin, smaller cubes, each measuring \(\frac{1}{2}\) foot on each side, are arranged to demonstrate how they might fit within the larger bin. The cubes fill the bin up to its edges, showing the possible arrangement and spacing.

**Question:**

What is the greatest number of boxes John can put into the bin?

**Options:**

- 14

(Note: The solution to this problem involves calculating the volume of the storage bin and dividing it by the volume of one cube to find the maximum number of boxes that fit.)
Transcribed Image Text:**Text:** John has a storage bin in the shape of a rectangular prism. The storage bin measures \(3 \frac{1}{2}\) feet long, 2 feet wide, and 2 feet tall. John will put boxes that measure \(\frac{1}{2}\) foot on each side into the bin. **Diagram Explanation:** The diagram illustrates a rectangular prism representing John's storage bin. The dimensions of the bin are marked: - Length: \(3 \frac{1}{2}\) feet - Width: 2 feet - Height: 2 feet Inside the bin, smaller cubes, each measuring \(\frac{1}{2}\) foot on each side, are arranged to demonstrate how they might fit within the larger bin. The cubes fill the bin up to its edges, showing the possible arrangement and spacing. **Question:** What is the greatest number of boxes John can put into the bin? **Options:** - 14 (Note: The solution to this problem involves calculating the volume of the storage bin and dividing it by the volume of one cube to find the maximum number of boxes that fit.)
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