Solution:
1. Convert the dimensions from mixed numbers to improper fractions or decimals:
* 3 1/2 inches = 3.5 inches
* 6 1/4 inches = 6.25 inches
* 4 inches = 4 inches
2. Use the formula for the volume of a rectangular box, which is the product of its length, width, and height:
V = \text{length} \times \text{width} \times \text{height}
V = 3.5 \text{ inches} \times 6.25 \text{ inches} \times 4 \text{ inches}
3. Calculate the volume:
V = 87.5 \text{ cubic inches}
The volume of the box is 87.5 cubic inches.