A cube has a volume `125cm^(3)`. Area of its one face is

Options

A. `25cm^(2)`
B. `30cm^(2)`
C. `5cm^(2)`
D. `20cm^(2)`

Answer

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

### Step-by-Step Solution:

1. **Understand 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.

2. **Given Volume**:
We know from the problem that the volume of the cube is \( 125 \, \text{cm}^3 \).

3. **Find the Length of One Side**:
To find the length of one side of the cube, we need to take the cube root of the volume:
\[ \text{side} = \sqrt[3]{V} = \sqrt[3]{125} \]
Calculating this gives:
\[ \text{side} = 5 \, \text{cm} \]

4. **Calculate the Area of One Face**:
The area \( A \) of one face of the cube (which is a square) is given by:
\[ A = \text{side}^2 \]
Substituting the value of the side:
\[ A = 5^2 = 25 \, \text{cm}^2 \]

5. **Conclusion**:
Therefore, the area of one face of the cube is \( 25 \, \text{cm}^2 \).

### Final Answer:
The area of one face of the cube is \( 25 \, \text{cm}^2 \).

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