The total surface area of a cube is ` 294 cm ^(2) ` find its volume

Answer

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

### Step 1: Understand the formula for the total surface area of a cube.
The total surface area (TSA) of a cube is given by the formula:
\[ \text{TSA} = 6a^2 \]
where \( a \) is the length of one side of the cube.

### Step 2: Set up the equation using the given total surface area.
We know from the problem that the total surface area of the cube is \( 294 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 294 \]

### Step 3: Solve for \( a^2 \).
To find \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{294}{6} \]
Calculating the right side:
\[ a^2 = 49 \]

### Step 4: Find the value of \( a \).
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{49} \]
\[ a = 7 \, \text{cm} \]

### Step 5: Calculate the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 7^3 \]
Calculating \( 7^3 \):
\[ V = 7 \times 7 \times 7 = 49 \times 7 = 343 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 343 \, \text{cm}^3 \).

---