Find the length of each edge of a cube. If its volume is
` 216 cm ^(3) `
(ii) ` 1.728 m ^(3)`

Answer

To find the length of each edge of a cube given its volume, we can use the formula for the volume of a cube, which is:

\[ V = a^3 \]

where \( V \) is the volume and \( a \) is the length of each edge.

### Part (i): Volume = 216 cm³

1. **Set up the equation**:
\[ a^3 = 216 \]

2. **Find the cube root**:
To find \( a \), we need to calculate the cube root of 216.
\[ a = \sqrt[3]{216} \]

3. **Calculate the cube root**:
The cube root of 216 is 6, since:
\[ 6 \times 6 \times 6 = 216 \]
Therefore,
\[ a = 6 \, \text{cm} \]

### Part (ii): Volume = 1.728 m³

1. **Set up the equation**:
\[ a^3 = 1.728 \]

2. **Find the cube root**:
To find \( a \), we need to calculate the cube root of 1.728.
\[ a = \sqrt[3]{1.728} \]

3. **Calculate the cube root**:
We can express 1.728 as \( 1.2^3 \), since:
\[ 1.2 \times 1.2 \times 1.2 = 1.728 \]
Therefore,
\[ a = 1.2 \, \text{m} \]

### Final Answers:
- For the first part, the length of each edge of the cube is **6 cm**.
- For the second part, the length of each edge of the cube is **1.2 m**.