Find the total surface area of the cube whose volume is `343cm^(3)`

Answer

To find the total surface area of a cube whose volume is \(343 \, \text{cm}^3\), we can follow these steps:

### Step 1: Understand the relationship between volume and side length of a cube
The volume \(V\) of a cube is given by the formula:
\[ V = s^3 \]
where \(s\) is the length of a side of the cube.

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

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

### Step 4: Use the side length to find the total surface area
The total surface area \(A\) of a cube is given by the formula:
\[ A = 6s^2 \]
Substituting the value of \(s\):
\[ A = 6 \times (7)^2 \]
Calculating \(7^2\):
\[ 7^2 = 49 \]
Now substituting back:
\[ A = 6 \times 49 \]
Calculating the total surface area:
\[ A = 294 \, \text{cm}^2 \]

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

---