The volume of a cube is numerically equal to sum of the length of its edges. The total surface area of cube in square units is :

Options

A. 72
B. 64.5
C. 12.4
D. 44.2

Explanation

To solve the problem, we need to find the total surface area of a cube given that its volume is numerically equal to the sum of the lengths of its edges.

### Step-by-Step Solution:

1. **Understanding the properties of a cube:**
- Let the length of each edge of the cube be \( A \).
- The volume \( V \) of the cube is given by the formula:
\[ V = A^3 \]
- The sum of the lengths of all the edges of the cube can be calculated as:
\[ \text{Sum of edges} = 12A \]
- This is because a cube has 12 edges.

2. **Setting up the equation:**
- According to the problem, the volume of the cube is numerically equal to the sum of the lengths of its edges:
\[ A^3 = 12A \]

3. **Rearranging the equation:**
- To solve for \( A \), we can rearrange the equation:
\[ A^3 - 12A = 0 \]
- Factoring out \( A \):
\[ A(A^2 - 12) = 0 \]

4. **Finding the values of \( A \):**
- This gives us two cases:
- \( A = 0 \) (not a valid solution for the length of an edge)
- \( A^2 - 12 = 0 \) which simplifies to:
\[ A^2 = 12 \implies A = \sqrt{12} = 2\sqrt{3} \]

5. **Calculating the total surface area:**
- The total surface area \( S \) of a cube is given by:
\[ S = 6A^2 \]
- Substituting \( A^2 = 12 \):
\[ S = 6 \times 12 = 72 \]

### Final Answer:
The total surface area of the cube is \( 72 \) square units.

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