To determine which box is large enough to hold all of the pillows with a total volume of [tex]\(8.5 \, ft^3\)[/tex], we will need to calculate the volume of each box and compare it to the given pillow volume.
### Step 1: Calculate the Volume of Box A
Box A has the following dimensions:
- Length: [tex]\(3 \, ft\)[/tex]
- Width: [tex]\(1.5 \, ft\)[/tex]
- Height: [tex]\(2 \, ft\)[/tex]
The formula for the volume of a rectangular box is:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Plugging in the dimensions for Box A:
[tex]\[ \text{Volume of Box A} = 3 \, ft \times 1.5 \, ft \times 2 \, ft \][/tex]
Calculate the volume step by step:
[tex]\[ 3 \times 1.5 = 4.5 \][/tex]
[tex]\[ 4.5 \times 2 = 9 \][/tex]
So, the volume of Box A is [tex]\(9 \, ft^3\)[/tex].
### Step 2: Calculate the Volume of Box B
Box B has the following dimensions:
- Length: [tex]\(2 \, ft\)[/tex]
- Width: [tex]\(2 \, ft\)[/tex]
- Height: [tex]\(1.5 \, ft\)[/tex]
Using the same volume formula:
[tex]\[ \text{Volume of Box B} = 2 \, ft \times 2 \, ft \times 1.5 \, ft \][/tex]
Calculate the volume step by step:
[tex]\[ 2 \times 2 = 4 \][/tex]
[tex]\[ 4 \times 1.5 = 6 \][/tex]
So, the volume of Box B is [tex]\(6 \, ft^3\)[/tex].
### Step 3: Compare Volumes to Pillow Volume
We need to compare the volumes of both boxes to the volume of the pillows, which is [tex]\(8.5 \, ft^3\)[/tex].
- Volume of Box A: [tex]\(9 \, ft^3\)[/tex]
- Volume of Box B: [tex]\(6 \, ft^3\)[/tex]
Now, we check which volume is greater than [tex]\(8.5 \, ft^3\)[/tex].
- Box A: [tex]\(9 > 8.5\)[/tex], so Box A is large enough.
- Box B: [tex]\(6 < 8.5\)[/tex], so Box B is not large enough.
### Conclusion
Since only Box A has a volume greater than [tex]\(8.5 \, ft^3\)[/tex], the correct answer is:
A. Box A
