To determine how many complete boxes can be wrapped with one roll of wrapping paper, we first need to calculate the surface area of the box and then the area of the wrapping paper.
- Calculate the surface area of the 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.
Given dimensions of the box:
- Length \(l = 16\) in.
- Width \(w = 14\) in.
- Height \(h = 6\) in.
Substituting the values into the formula:
\[ A = 2(16 \cdot 14 + 16 \cdot 6 + 14 \cdot 6) \]
First, calculate each product:
- \(16 \cdot 14 = 224\) in²
- \(16 \cdot 6 = 96\) in²
- \(14 \cdot 6 = 84\) in²
Now, add these areas together:
\[ 224 + 96 + 84 = 404 \text{ in}^2 \]
Now, multiply by 2:
\[ A = 2 \cdot 404 = 808 \text{ in}^2 \]
So the surface area of one box is \(808\) square inches.
- Calculate the area of the wrapping paper:
The dimensions of the roll of wrapping paper are \(25\) in. by \(405\) in.
The area \(A_w\) of the wrapping paper is:
\[ A_w = 25 \cdot 405 \]
Calculating this:
\[ A_w = 25 \cdot 405 = 10125 \text{ in}^2 \]
- Determine how many complete boxes can be wrapped:
Now, we find how many complete boxes can be wrapped with the total area of the wrapping paper:
\[ \text{Number of boxes} = \frac{\text{Area of wrapping paper}}{\text{Surface area of one box}} = \frac{10125}{808} \]
Calculating this gives:
\[ \frac{10125}{808} \approx 12.5 \]
Since we can only wrap complete boxes, we take the integer part:
The number of complete boxes that can be wrapped is \(12\).
Thus, the final answer is:
12 boxes.
3 answers