The diagonal of a cube is 2`sqrt3` cm. Find the surface area of the cube.

Options

A. 15 sq cm
B. 18 sq cm
C. 25 sq cm
D. 24 sq cm

Answer

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

### Step-by-Step Solution:

1. **Identify the formula for the diagonal of a cube**:
The formula for the diagonal \(d\) of a cube with side length \(s\) is given by:
\[ d = s\sqrt{3} \]

2. **Substitute the given diagonal into the formula**:
We know from the problem that the diagonal \(d\) is \(2\sqrt{3}\) cm. So we can set up the equation:
\[ 2\sqrt{3} = s\sqrt{3} \]

3. **Solve for the side length \(s\)**:
To isolate \(s\), divide both sides of the equation by \(\sqrt{3}\):
\[ s = \frac{2\sqrt{3}}{\sqrt{3}} = 2 \text{ cm} \]

4. **Use the side length to find the surface area**:
The formula for the surface area \(A\) of a cube is:
\[ A = 6s^2 \]
Now substitute \(s = 2\) cm into the formula:
\[ A = 6(2^2) = 6 \times 4 = 24 \text{ cm}^2 \]

5. **Conclusion**:
The surface area of the cube is \(24 \text{ cm}^2\).