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The width of a box is one third of its length. The height of the box is one third of its width. If the length of the box is 27 cm, what is the volume of the box?

A. [tex]$81 \text{ cm}^3$[/tex]
B. [tex]$162 \text{ cm}^3$[/tex]
C. [tex]$243 \text{ cm}^3$[/tex]
D. [tex]$729 \text{ cm}^3$[/tex]


Sagot :

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]