Find the volume of a cube whose surface area is 54 square meter

Options

A. `27m^3`
B. `9m^3`
C. `16^3`
D. `81m^3`

Answer

To find the volume of a cube whose surface area is 54 square meters, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Surface Area of a Cube**:
The surface area (SA) of a cube is given by the formula:
\[ SA = 6A^2 \]
where \( A \) is the length of one side of the cube.

2. **Set Up the Equation**:
We know the surface area is 54 square meters. Therefore, we can set up the equation:
\[ 6A^2 = 54 \]

3. **Solve for \( A^2 \)**:
To isolate \( A^2 \), divide both sides of the equation by 6:
\[ A^2 = \frac{54}{6} \]
Simplifying this gives:
\[ A^2 = 9 \]

4. **Find the Length of One Side \( A \)**:
Now, take the square root of both sides to find \( A \):
\[ A = \sqrt{9} = 3 \text{ meters} \]

5. **Calculate the Volume of the Cube**:
The volume (V) of a cube is given by the formula:
\[ V = A^3 \]
Substituting the value of \( A \):
\[ V = 3^3 = 27 \text{ cubic meters} \]

### Final Answer:
The volume of the cube is **27 cubic meters**.

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