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 need to first calculate the surface area of both the roll of wrapping paper and the boxes.

### Step 1: Calculate the surface area of one box
The surface area \( A \) of a rectangular box can be calculated using the formula:

\[
A = 2(lw + lh + wh)
\]

where \( l \), \( w \), and \( h \) are the length, width, and height of the box respectively.

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

Plugging in these values:

\[
A = 2(16 \times 14 + 16 \times 6 + 14 \times 6)
\]

Calculating each term inside the parentheses:

1. \( 16 \times 14 = 224 \)
2. \( 16 \times 6 = 96 \)
3. \( 14 \times 6 = 84 \)

Now add these together:

\[
224 + 96 + 84 = 404
\]

Now, calculate the total surface area:

\[
A = 2 \times 404 = 808 \text{ square inches}
\]

### Step 2: Calculate the area of the roll of wrapping paper
The area \( A_p \) of the roll of wrapping paper can be calculated as follows:

\[
A_p = \text{length} \times \text{width}
\]

Given the dimensions of the wrapping paper:
- Length = 405 in.
- Width = 25 in.

Calculating the area:

\[
A_p = 405 \times 25 = 10125 \text{ square inches}
\]

### Step 3: Calculate how many boxes can be wrapped
To find out how many boxes can be wrapped with the roll of wrapping paper, we divide the area of the wrapping paper by the surface area of one box:

\[
\text{Number of boxes} = \frac{A_p}{\text{Surface area of one box}} = \frac{10125}{808}
\]

Calculating this:

\[
\frac{10125}{808} \approx 12.5
\]

Since we can only wrap complete boxes, we take the whole number part:

\[
\text{Number of complete boxes} = 12
\]

### Conclusion
Therefore, **12 complete boxes can be wrapped with one roll of wrapping paper.**