Question

A roll of wrapping paper measures 25 in.×405 in.
The boxes being wrapped are 16 in.×14 in.×6 in.
How many complete boxes can be wrapped with one roll of wrapping paper?(1 point)

Answer 1

To determine how many complete boxes can be wrapped with one roll of wrapping paper, we first need to calculate the surface area of both the wrapping paper and the boxes.

1. **Calculate the surface area of the box:**
A box has a surface area given by the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the box.

For the given box dimensions:
- Length \( l = 16 \) in
- Width \( w = 14 \) in
- Height \( h = 6 \) in

Now, substituting in the values:
\[
\text{Surface Area} = 2(16 \cdot 14 + 16 \cdot 6 + 14 \cdot 6)
\]
- \( 16 \cdot 14 = 224 \)
- \( 16 \cdot 6 = 96 \)
- \( 14 \cdot 6 = 84 \)

Adding those:
\[
224 + 96 + 84 = 404
\]
So the surface area is:
\[
\text{Surface Area} = 2 \cdot 404 = 808 \text{ square inches}
\]

2. **Calculate the surface area of the wrapping paper roll:**
The roll of wrapping paper is 25 in. wide and 405 in. long. Therefore, the total surface area is:
\[
\text{Surface Area of the Wrapping Paper} = \text{width} \times \text{length} = 25 \text{ in} \times 405 \text{ in} = 10125 \text{ square inches}
\]

3. **Determine how many boxes can be wrapped:**
Now we can find out how many complete boxes can be wrapped by dividing the surface area of the wrapping paper by the surface area of a single box:
\[
\text{Number of boxes} = \frac{\text{Surface Area of the Wrapping Paper}}{\text{Surface Area of One Box}} = \frac{10125}{808}
\]

Calculating that gives:
\[
\text{Number of boxes} \approx 12.5
\]
Since we can only wrap complete boxes, we can wrap **12 complete boxes** with the roll of wrapping paper.

The final answer is:
\[
\boxed{12}
\]