If the area of a face of a cube is `10 cm^(2)`, then the total surface area of the cube is __________.

Answer

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

### Step-by-Step Solution:

1. **Understand the properties of a cube**:
A cube has 6 faces, and each face is a square. The area of a square is calculated using the formula:
\[ \text{Area} = \text{side} \times \text{side} = a^2 \]
where \( a \) is the length of one side of the square.

2. **Identify the area of one face**:
According to the problem, the area of one face of the cube is given as \( 10 \, \text{cm}^2 \). Therefore, we can write:
\[ a^2 = 10 \]

3. **Calculate the total surface area of the cube**:
The total surface area (TSA) of a cube is given by the formula:
\[ \text{TSA} = 6 \times (\text{Area of one face}) = 6a^2 \]
Since we know \( a^2 = 10 \):
\[ \text{TSA} = 6 \times 10 = 60 \, \text{cm}^2 \]

4. **Final answer**:
Therefore, the total surface area of the cube is:
\[ \text{Total Surface Area} = 60 \, \text{cm}^2 \]