To determine how many complete boxes can be wrapped with one roll of wrapping paper, we first need to find the surface area of the boxes and the total area of the wrapping paper.
- Calculate the surface area of one box.
The dimensions of the box are 16 in. × 14 in. × 6 in.
The formula for the surface area (SA) of a rectangular box is given by:
\[ SA = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the length, width, and height of the box, respectively.
Substituting the dimensions of the box:
\[ SA = 2(16 \times 14 + 16 \times 6 + 14 \times 6) \]
Calculating each term inside the parentheses:
- \( 16 \times 14 = 224 \)
- \( 16 \times 6 = 96 \)
- \( 14 \times 6 = 84 \)
Now add them together:
\[ 224 + 96 + 84 = 404 \]
Now multiply by 2:
\[ SA = 2 \times 404 = 808 \text{ square inches} \]
- Calculate the area of the roll of wrapping paper.
The dimensions of the wrapping paper are 25 in. × 405 in.
The area (A) of the wrapping paper is given by:
\[ A = 25 \times 405 \]
Calculating the area:
\[ A = 25 \times 405 = 10125 \text{ square inches} \]
- Determine how many complete boxes can be wrapped.
To find how many complete boxes can be wrapped, we divide the area of the wrapping paper by the surface area of one box:
\[ \text{Number of boxes} = \frac{A}{SA} = \frac{10125}{808} \]
Calculating this gives:
\[ \frac{10125}{808} \approx 12.5 \]
Since only whole boxes can be wrapped, we take the floor of this value:
\[ \text{Number of complete boxes} = 12 \]
Thus, the number of complete boxes that can be wrapped with one roll of wrapping paper is 12.
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