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

Options

A. `25 cm ^(2)`
B. ` 30 cm ^(2)`
C. ` 5 cm ^(2)`
D. ` 20 cm ^(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 the volume of the cube is \( 125 \, \text{cm}^3 \).

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

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

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

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

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