If the side of a cube is `2 sqrt""3cm`, then find the total surface area of the cube

Options

A. `96cm^(2)`
B. `72cm^(2)`
C. `48cm^(2)`
D. `60cm^(2)`

Answer

To find the total surface area of a cube when the side length is given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the side length of the cube**:
The side length of the cube is given as \( 2\sqrt{3} \) cm.

2. **Recall the formula for the total surface area of a cube**:
The total surface area (TSA) of a cube can be calculated using the formula:
\[ \text{TSA} = 6 \times (\text{side length})^2 \]

3. **Substitute the side length into the formula**:
Substitute \( 2\sqrt{3} \) cm into the formula:
\[ \text{TSA} = 6 \times (2\sqrt{3})^2 \]

4. **Calculate \( (2\sqrt{3})^2 \)**:
First, calculate \( (2\sqrt{3})^2 \):
\[ (2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12 \]

5. **Multiply by 6**:
Now, substitute back into the TSA formula:
\[ \text{TSA} = 6 \times 12 = 72 \text{ cm}^2 \]

6. **Final Answer**:
The total surface area of the cube is \( 72 \text{ cm}^2 \).