The perimeter of one face of a cube is 20 cm. Its volume will be

Options

A. `625 cm^(3)`
B. `100 cm^(3)`
C. `125 cm^(3)`
D. `400 cm^(3)`

Answer

To find the volume of a cube when the perimeter of one face is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Shape**:
A cube has six faces, and each face is a square.

2. **Identify the Perimeter of One Face**:
The perimeter of one face of the cube is given as 20 cm.

3. **Use the Formula for Perimeter**:
The perimeter \( P \) of a square is calculated using the formula:
\[ P = 4a \]
where \( a \) is the length of one side of the square.

4. **Set Up the Equation**:
Given that the perimeter is 20 cm, we can set up the equation:
\[ 4a = 20 \]

5. **Solve for the Side Length \( a \)**:
To find \( a \), divide both sides of the equation by 4:
\[ a = \frac{20}{4} = 5 \text{ cm} \]

6. **Calculate the Volume of the Cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 5^3 = 5 \times 5 \times 5 = 125 \text{ cm}^3 \]

### Final Answer:
The volume of the cube is **125 cm³**.

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