To find the length of the diagonal [tex]\(a\)[/tex] of a cube with edges of 5 cm, we follow these steps:
1. Identify the given information:
- The edge length of the cube is given as 5 cm.
2. Use the formula for the space diagonal of a cube:
The formula for calculating the length of the space diagonal (or body diagonal) of a cube is:
[tex]\[
a = s \sqrt{3}
\][/tex]
where:
- [tex]\(a\)[/tex] is the length of the diagonal,
- [tex]\(s\)[/tex] is the length of the edge of the cube,
- [tex]\(\sqrt{3}\)[/tex] is a constant that comes from the geometric properties of a cube.
3. Substitute the given edge length into the formula:
[tex]\[
a = 5 \times \sqrt{3}
\][/tex]
4. Calculate the numerical value:
- Given that [tex]\(\sqrt{3} \approx 1.732\)[/tex], multiply this value by the edge length of 5 cm.
5. Arrive at the final result:
- The length of the diagonal [tex]\(a\)[/tex] of the cube is [tex]\(\approx 8.660\)[/tex] cm.
Therefore, the length of the diagonal of the cube with 5 cm edges is approximately 8.66 cm.
