To find the volume of the styrofoam peanuts in the shipping box, we first need to calculate the volume of the shipping box and then subtract the volume of the two gifts.
Step 1: Calculate the volume of the shipping box.
The dimensions of the shipping box are:
- Length = 12 inches
- Width = 5 inches
- Height = 5 inches
The volume \( V \) of a rectangular box is calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Calculating the volume of the shipping box:
\[ V = 12 , \text{inches} \times 5 , \text{inches} \times 5 , \text{inches} = 300 , \text{cubic inches} \]
Step 2: Calculate the volume of the puzzle cube.
The volume of a cube is calculated using the formula:
\[ V = \text{side length}^3 \]
The side length of the puzzle cube is 4 inches:
\[ V = 4 , \text{inches} \times 4 , \text{inches} \times 4 , \text{inches} = 64 , \text{cubic inches} \]
Step 3: Calculate the volume of the card game box.
The dimensions of the card game box are:
- Length = 6 inches
- Width = 4 inches
- Height = 4.5 inches
Calculating the volume of the card game box:
\[ V = 6 , \text{inches} \times 4 , \text{inches} \times 4.5 , \text{inches} = 108 , \text{cubic inches} \]
Step 4: Calculate the total volume of the gifts.
Now, we add the volumes of both gifts:
\[ \text{Total volume of gifts} = 64 , \text{cubic inches} + 108 , \text{cubic inches} = 172 , \text{cubic inches} \]
Step 5: Calculate the volume of the styrofoam peanuts.
Finally, we subtract the total volume of the gifts from the volume of the shipping box to find the volume of the styrofoam peanuts:
\[ \text{Volume of styrofoam peanuts} = \text{Volume of shipping box} - \text{Total volume of gifts} \]
\[ \text{Volume of styrofoam peanuts} = 300 , \text{cubic inches} - 172 , \text{cubic inches} = 128 , \text{cubic inches} \]
Therefore, the volume of the styrofoam "peanuts" in the shipping box is 128 cubic inches.
1 answer