If the volume of a cube is `1331 cm^3` , then find the length of its edge.

Answer

To find the length of the edge of a cube when the volume is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the volume of a cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = A^3 \]
where \( A \) is the length of an edge of the cube.

2. **Substitute the given volume into the formula**:
We know that the volume \( V \) is \( 1331 \, \text{cm}^3 \). So we can write:
\[ 1331 = A^3 \]

3. **Take the cube root of both sides**:
To find the length of the edge \( A \), we need to take the cube root of \( 1331 \):
\[ A = \sqrt[3]{1331} \]

4. **Factorize \( 1331 \)**:
To find the cube root, we can factor \( 1331 \):
- Start dividing \( 1331 \) by \( 11 \):
\[ 1331 \div 11 = 121 \]
- Next, divide \( 121 \) by \( 11 \):
\[ 121 \div 11 = 11 \]
- Finally, divide \( 11 \) by \( 11 \):
\[ 11 \div 11 = 1 \]
This gives us the prime factorization:
\[ 1331 = 11 \times 11 \times 11 = 11^3 \]

5. **Calculate the cube root**:
Since \( 1331 = 11^3 \), we can find the cube root:
\[ A = \sqrt[3]{11^3} = 11 \]

6. **State the final answer**:
Therefore, the length of the edge of the cube is:
\[ A = 11 \, \text{cm} \]

### Final Answer:
The length of the edge of the cube is \( 11 \, \text{cm} \).

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