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

Answer

To find the length of an edge of a cube when the surface area is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the surface area of a cube**:
The surface area (SA) of a cube is calculated using the formula:
\[ SA = 6a^2 \]
where \( a \) is the length of an edge of the cube.

2. **Set up the equation with the given surface area**:
According to the problem, the surface area of the cube is \( 294 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 294 \]

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

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

5. **Conclusion**:
The length of an edge of the cube is \( 7 \, \text{cm} \).