Find the total surface area of a cube whose diagonal is of length `4sqrt(3)` cm .

Answer

To find the total surface area of a cube whose diagonal is of length \(4\sqrt{3}\) cm, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side length of the cube.
The diagonal \(d\) of a cube can be expressed in terms of the side length \(a\) using the formula:
\[ d = a\sqrt{3} \]
where \(a\) is the length of one edge of the cube.

### Step 2: Set up the equation using the given diagonal.
We know the diagonal \(d\) is \(4\sqrt{3}\) cm. Therefore, we can set up the equation:
\[ 4\sqrt{3} = a\sqrt{3} \]

### Step 3: Solve for the side length \(a\).
To find \(a\), we can divide both sides of the equation by \(\sqrt{3}\):
\[ a = 4 \text{ cm} \]

### Step 4: Calculate the total surface area of the cube.
The total surface area \(A\) of a cube is given by the formula:
\[ A = 6a^2 \]
Substituting the value of \(a\):
\[ A = 6 \times (4)^2 \]
\[ A = 6 \times 16 \]
\[ A = 96 \text{ cm}^2 \]

### Final Answer:
The total surface area of the cube is \(96 \text{ cm}^2\).

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