The surface area of a cube is 384 `m^2`. Its volume will be

Options

A. `343 m^2`
B. `616m^2`
C. `512 m^3`
D. `660 m^3`

Answer

To find the volume of a cube when given its surface area, 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:
\[ \text{SA} = 6a^2 \]
where \( a \) is the length of one side of the cube.

### Step 2: Set up the equation using the given surface area.
We know the surface area is 384 m². Therefore, we can set up the equation:
\[ 6a^2 = 384 \]

### Step 3: Solve for \( a^2 \).
To find \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{384}{6} \]
\[ a^2 = 64 \]

### Step 4: Solve for \( a \).
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{64} \]
\[ a = 8 \, \text{m} \]

### Step 5: Calculate the volume of the cube.
The volume (V) of a cube is given by the formula:
\[ V = a^3 \]
Now substitute \( a = 8 \):
\[ V = 8^3 \]
\[ V = 512 \, \text{m}^3 \]

### Final Answer:
The volume of the cube is \( 512 \, \text{m}^3 \).

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