The volume of a cube is 343 `cm^(3)`. Find its total surface area.

Answer

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

### Step 1: Understand the formula for the volume of a cube
The volume \( V \) of a cube is given by the formula:
\[ V = \text{side}^3 \]
where "side" is the length of one edge of the cube.

### Step 2: Set up the equation using the given volume
We know the volume of the cube is \( 343 \, \text{cm}^3 \). Therefore, we can write:
\[ \text{side}^3 = 343 \]

### Step 3: Calculate the side length of the cube
To find the side length, we need to take the cube root of \( 343 \):
\[ \text{side} = \sqrt[3]{343} \]
Calculating the cube root, we find:
\[ \text{side} = 7 \, \text{cm} \]

### Step 4: Understand the formula for the total surface area of a cube
The total surface area \( A \) of a cube is given by the formula:
\[ A = 6 \times \text{side}^2 \]

### Step 5: Calculate the total surface area using the side length
Now that we have the side length, we can find the total surface area:
\[ A = 6 \times (7 \, \text{cm})^2 \]
Calculating \( (7 \, \text{cm})^2 \):
\[ (7 \, \text{cm})^2 = 49 \, \text{cm}^2 \]
Now substituting back into the surface area formula:
\[ A = 6 \times 49 \, \text{cm}^2 = 294 \, \text{cm}^2 \]

### Final Answer
The total surface area of the cube is \( 294 \, \text{cm}^2 \).

---