The total surface area of cube is ` 216 cm ^(2)` Find its volume.

Answer

To solve the problem of finding the volume of a cube given its total surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
The total surface area (TSA) of the cube is given as \( 216 \, \text{cm}^2 \).

2. **Recall the formula for the total surface area of a cube**:
The formula for the total surface area of a cube is:
\[ \text{TSA} = 6 \times \text{side}^2 \]
Let the side of the cube be denoted as \( x \).

3. **Set up the equation**:
According to the problem, we can set up the equation:
\[ 6x^2 = 216 \]

4. **Solve for \( x^2 \)**:
To isolate \( x^2 \), divide both sides of the equation by 6:
\[ x^2 = \frac{216}{6} \]
\[ x^2 = 36 \]

5. **Find \( x \)**:
To find the side length \( x \), take the square root of both sides:
\[ x = \sqrt{36} \]
\[ x = 6 \, \text{cm} \]

6. **Calculate the volume of the cube**:
The formula for the volume \( V \) of a cube is:
\[ V = \text{side}^3 \]
Substituting the value of \( x \):
\[ V = 6^3 \]
\[ V = 6 \times 6 \times 6 = 216 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 216 \, \text{cm}^3 \).