What is the maximum number of boxes with dimensions 2 inches by 3 inches by 4 inches that could fit in a cube-shaped container that has a volume of 1 cubic foot?

Answer

To find the maximum number of boxes with dimensions 2 inches by 3 inches by 4 inches that can fit inside a cube-shaped container with a volume of 1 cubic foot, we will follow these steps:

### Step 1: Convert the volume of the cube-shaped container from cubic feet to cubic inches.
1. We know that 1 foot is equal to 12 inches.
2. Therefore, the volume of the cube-shaped container in cubic inches is calculated as:
\[ \text{Volume} = 1 \text{ cubic foot} = 12 \text{ inches} \times 12 \text{ inches} \times 12 \text{ inches} = 1728 \text{ cubic inches} \]

### Step 2: Calculate the volume of one small box.
1. The dimensions of the box are given as 2 inches, 3 inches, and 4 inches.
2. The volume of the box is calculated as:
\[ \text{Volume of one box} = 2 \text{ inches} \times 3 \text{ inches} \times 4 \text{ inches} = 24 \text{ cubic inches} \]

### Step 3: Determine the maximum number of boxes that can fit in the container.
1. To find the maximum number of boxes that can fit in the container, divide the volume of the container by the volume of one box:
\[ \text{Number of boxes} = \frac{\text{Volume of the container}}{\text{Volume of one box}} = \frac{1728 \text{ cubic inches}}{24 \text{ cubic inches}} = 72 \]

### Conclusion:
The maximum number of boxes that can fit in the cube-shaped container is **72**.

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