The surface area of a cube is `294 cm^(2) ` . Find :
volume of the cube :

Answer

To solve the problem of finding the volume of a cube given its surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the surface area of a cube**:
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]
where \( a \) is the length of one side of the cube.

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

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

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

5. **Calculate the volume of the cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substitute \( a = 7 \):
\[ V = 7^3 = 343 \, \text{cm}^3 \]

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

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