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Q12. The volume of material used to make a cube is [tex]4913 \, \text{cm}^3[/tex]. What is the length of the edge of the cube?

Sagot :

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.