To determine how many boxes Montana can wrap with her available wrapping paper, we first need to calculate the surface area of a single box and then see how many boxes can be wrapped using the available wrapping paper.
Step 1: Calculate the surface area of one box.
The box has the following dimensions:
- Width = 6 inches
- Length = 10 inches
- Height = 2 inches
The surface area \(A\) of a rectangular box can be calculated using the formula:
\[ A = 2lw + 2lh + 2wh \]
Where:
- \(l\) = length
- \(w\) = width
- \(h\) = height
Substituting the values:
\[ A = 2(10 , \text{in})(6 , \text{in}) + 2(10 , \text{in})(2 , \text{in}) + 2(6 , \text{in})(2 , \text{in}) \]
Calculating each term:
- \(2(10)(6) = 120 , \text{in}^2\)
- \(2(10)(2) = 40 , \text{in}^2\)
- \(2(6)(2) = 24 , \text{in}^2\)
Adding these together gives:
\[ A = 120 + 40 + 24 = 184 , \text{in}^2 \]
Step 2: Calculate how many boxes can be wrapped with 600 in² of wrapping paper.
To find out how many boxes can be wrapped, we divide the total amount of wrapping paper by the surface area of one box:
\[ \text{Number of boxes} = \frac{\text{Total wrapping paper}}{\text{Surface area of one box}} = \frac{600 , \text{in}^2}{184 , \text{in}^2} \]
Calculating this:
\[ \text{Number of boxes} \approx 3.26 \]
Since we can only wrap whole boxes, we take the lowest whole number, which is 3.
Conclusion
Montana can wrap 3 boxes with her wrapping paper.