If the volume of a cube is `"512 cm"^(3)`, then the length of the edge is __________.

Options

A. 7 cm
B. 8 cm
C. 4 cm
D. 12 cm

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:
\[ V = \text{side}^3 \]
where "side" is the length of an edge of the cube.

2. **Set up the equation**:
We know the volume of the cube is \( 512 \, \text{cm}^3 \). Therefore, we can write:
\[ \text{side}^3 = 512 \]

3. **Find the cube root**:
To find the length of the edge (side), we need to take the cube root of both sides of the equation:
\[ \text{side} = \sqrt[3]{512} \]

4. **Calculate the cube root**:
We can simplify \( 512 \) as follows:
\[ 512 = 8 \times 8 \times 8 = 8^3 \]
Therefore:
\[ \text{side} = \sqrt[3]{8^3} = 8 \]

5. **State the final answer**:
The length of the edge of the cube is:
\[ \text{side} = 8 \, \text{cm} \]

### Final Answer:
The length of the edge is **8 cm**.

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