Certainly! Let's solve the problem of finding the length of the edge of a cube given its volume.
### Problem
The volume of a material used to make a cube is 4913 cm³. We need to determine the length of each edge of the cube.
### Step-by-Step Solution
1. Understand the Volume Formula:
The volume [tex]\( V \)[/tex] of a cube can be expressed by the formula:
[tex]\[
V = a^3
\][/tex]
where [tex]\( a \)[/tex] is the length of one edge of the cube.
2. Given Information:
We are given that the volume [tex]\( V \)[/tex] of the cube is 4913 cm³.
3. Set Up the Equation:
Using the volume formula, we set it equal to the given volume:
[tex]\[
a^3 = 4913
\][/tex]
4. Solve for [tex]\( a \)[/tex]:
To find the length of the edge [tex]\( a \)[/tex], we need to take the cube root of 4913:
[tex]\[
a = \sqrt[3]{4913}
\][/tex]
5. Calculation of Cube Root:
By calculating the cube root of 4913, we find:
[tex]\[
\sqrt[3]{4913} \approx 17
\][/tex]
### Conclusion
Therefore, the length of each edge of the cube is approximately 17 cm.
