To solve the problem, let's proceed step-by-step to find the dimensions of the box and then compute its volume.
1. Given: The length of the box is 27 cm.
2. Width Calculation:
- The width of the box is one third of its length.
- Therefore, the width = [tex]\(\frac{1}{3}\)[/tex] length.
- Substituting the given length:
- width = [tex]\(\frac{1}{3}\)[/tex] 27 cm = 9 cm.
3. Height Calculation:
- The height of the box is one third of its width.
- Therefore, the height = [tex]\(\frac{1}{3}\)[/tex] width.
- Substituting the calculated width:
- height = [tex]\(\frac{1}{3}\)[/tex] 9 cm = 3 cm.
4. Volume Calculation:
- The volume of a rectangular box is calculated by multiplying its length, width, and height.
- Volume = length × width × height.
- Substituting the dimensions we found:
- Volume = 27 cm 9 cm 3 cm = 729 cm³.
So, the volume of the box is [tex]\(729 \, \text{cm}^3\)[/tex].
The correct answer is:
D. [tex]\(729 \, \text{cm}^3\)[/tex]
