The total surface area of a cube is `96 cm^(2)`. The volume of the cube is

Options

A. `8cm^(3)`
B. `512cm^(3)`
C. `64cm^(3)`
D. `27 cm^(3)`

Explanation

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

### Step 1: Understand the formula for the total surface area of a cube.
The total surface area (TSA) of a cube is given by the formula:
\[ \text{TSA} = 6a^2 \]
where \( a \) is the length of one side of the cube.

### Step 2: Set up the equation using the given total surface area.
We know from the problem that the total surface area is \( 96 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 96 \]

### Step 3: Solve for \( a^2 \).
To find \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{96}{6} = 16 \, \text{cm}^2 \]

### Step 4: Find the value of \( a \).
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{16} = 4 \, \text{cm} \]

### 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 \( a \):
\[ V = 4^3 = 4 \times 4 \times 4 = 64 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 64 \, \text{cm}^3 \).

---