If the surface area of a cube is 1944 `m^2`, its volume is:

Options

A. `4912 m^3`
B. `1648 m^3`
C. `2744 m^3`
D. `5832 m^3`

Answer

To find the volume of a cube when the surface area is given, we can follow these steps:

### Step 1: Understand the formula for the 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.

### Step 2: Set up the equation with the given surface area.
We know from the problem that the surface area of the cube is \( 1944 \, m^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 1944 \]

### Step 3: Solve for \( a^2 \).
To find \( a^2 \), we divide both sides of the equation by 6:
\[ a^2 = \frac{1944}{6} \]
Calculating the right side:
\[ a^2 = 324 \]

### Step 4: Solve for \( a \).
Now, we take the square root of both sides to find \( a \):
\[ a = \sqrt{324} \]
Calculating the square root:
\[ a = 18 \, m \]

### Step 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 \( a \):
\[ V = 18^3 \]
Calculating \( 18^3 \):
\[ V = 5832 \, m^3 \]

### Final Answer:
The volume of the cube is \( 5832 \, m^3 \).

---