To solve the problem, let's carefully break down the steps:
1. Understanding the Cube's Properties:
- A cube has 12 edges.
- The sum of the lengths of all these edges is given as 6 cm.
2. Calculating the Length of One Edge:
- If the total length of all 12 edges is 6 cm, we can find the length of one edge by dividing the total length by the number of edges:
[tex]\[
\text{Length of one edge} = \frac{\text{Total length of all edges}}{\text{Number of edges}} = \frac{6 \text{ cm}}{12} = 0.5 \text{ cm}
\][/tex]
3. Calculating the Volume of the Cube:
- The volume of a cube is found by raising the edge length to the power of three (since volume is edge length cubed):
[tex]\[
\text{Volume} = (\text{Edge length})^3 = (0.5 \text{ cm})^3
\][/tex]
- Calculating this:
[tex]\[
(0.5)^3 = 0.5 \times 0.5 \times 0.5 = 0.125 \text{ cubic cm}
\][/tex]
4. Concluding the Volume:
- Therefore, the volume of the cube is:
[tex]\[
0.125 \text{ cubic cm}
\][/tex]
5. Multiple-Choice Answer:
- Looking at the provided options:
a. 118
b. [tex]\( \frac{1}{4} \)[/tex]
c. [tex]\( \frac{1}{2} \)[/tex]
d. 1
- The volume 0.125 cubic cm is equivalent to [tex]\( \frac{1}{8} \)[/tex].
- None of these directly match [tex]\( \frac{1}{8} \)[/tex].
Since none of the given options exactly match the correct calculation ([tex]\(\frac{1}{8}\)[/tex]), it appears there might be a mistake in the provided choices. But based on the detailed calculations we've done and interpreting the numerical result correctly, the volume of the cube is indeed [tex]\( \boxed{0.125} \)[/tex] cubic centimeters.
