To find the volume of the box, we first need to determine its dimensions based on the relationships provided:
- Width of the box (W): 5 cm
- Length of the box (L) is 2 cm greater than the width: \[ L = W + 2 = 5 + 2 = 7 \text{ cm} \]
- Height of the box (H) is 2 cm greater than the length: \[ H = L + 2 = 7 + 2 = 9 \text{ cm} \]
Now we have:
- Width (W) = 5 cm
- Length (L) = 7 cm
- Height (H) = 9 cm
The volume \( V \) of a right rectangular prism is calculated as: \[ V = L \times W \times H \] Substituting the values we found: \[ V = 7 \times 5 \times 9 \]
Calculating it step by step:
- \( 7 \times 5 = 35 \)
- \( 35 \times 9 = 315 \)
Thus, the volume of the box is: \[ \text{Volume} = 315 \text{ cm}^3 \]
Therefore, the answer is: 315 cm³ (315 cm cubed).