The volume of a cube is 9261 `m^(2)`, then area of one face of the cube will be

Options

A. 216 `m^(2)`
B. 36 `m^(2)`
C. 441 `m^(2)`
D. 24 `m^(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 relationship between volume and side length of a cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = s^3 \]
where \( s \) is the length of one side of the cube.

2. **Set up the equation with the given volume**:
Given that the volume of the cube is \( 9261 \, m^3 \), we can write:
\[ s^3 = 9261 \]

3. **Calculate the cube root to find the side length**:
To find \( s \), we need to calculate the cube root of \( 9261 \):
\[ s = \sqrt[3]{9261} \]

4. **Factor the number to find the cube root**:
We can factor \( 9261 \) to find its prime factors:
- Check divisibility by \( 3 \):
- \( 9261 \div 3 = 3087 \)
- \( 3087 \div 3 = 1029 \)
- \( 1029 \div 3 = 343 \)
- Now, \( 343 \) can be expressed as \( 7^3 \):
\[ 9261 = 3^3 \times 7^3 \]

5. **Combine the cube roots**:
Now, we can take the cube root of both sides:
\[ s = \sqrt[3]{3^3 \times 7^3} = 3 \times 7 = 21 \, m \]

6. **Calculate the area of one face of the cube**:
The area \( A \) of one face of the cube is given by:
\[ A = s^2 \]
Substituting the value of \( s \):
\[ A = 21^2 = 441 \, m^2 \]

### Final Answer:
The area of one face of the cube is \( 441 \, m^2 \).

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