Question

Mia put two gifts in a shipping box, then filled the box with styrofoam "peanuts".

The dimensions of the shipping box were 12
inches by 5
inches by 5
inches.
One gift was a puzzle cube with a side length of 4
inches.
One gift was a card game that was in a box with dimensions 6
inches by 4
inches by 4 1/2


inches.
What was the volume of the styrofoam "peanuts" in the shipping box?

Answer 1

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**.