If the length of diagonal of a cube is `8 sqrt3`cm then its surface area is

Options

A. `192 cm^(2)`
B. `384 cm^(2)`
C. `512 cm^(2)`
D. `768 cm^(2)`

Explanation

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

### Step-by-Step Solution:

1. **Understand the relationship between the diagonal and the side of the cube:**
The diagonal \(d\) of a cube with side length \(A\) can be expressed using the formula:
\[ d = A \sqrt{3} \]

2. **Set up the equation with the given diagonal:**
According to the problem, the diagonal \(d\) is given as \(8 \sqrt{3}\) cm. Therefore, we can set up the equation:
\[ A \sqrt{3} = 8 \sqrt{3} \]

3. **Solve for the side length \(A\):**
To find \(A\), we can divide both sides of the equation by \(\sqrt{3}\):
\[ A = 8 \text{ cm} \]

4. **Calculate the surface area of the cube:**
The surface area \(S\) of a cube is given by the formula:
\[ S = 6A^2 \]
Substituting \(A = 8\) cm into the formula:
\[ S = 6 \times (8)^2 \]
\[ S = 6 \times 64 \]
\[ S = 384 \text{ cm}^2 \]

5. **Final answer:**
The surface area of the cube is \(384 \text{ cm}^2\).