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 the cube given its total surface area, 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:
\[ \text{TSA} = 6 \times \text{side}^2 \]

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

### Step 3: Solve for the side length of the cube.
To find the side length, we first divide both sides of the equation by 6:
\[ \text{side}^2 = \frac{96}{6} \]
Calculating the right side:
\[ \text{side}^2 = 16 \]

### Step 4: Take the square root to find the side length.
To find the side length, we take the square root of both sides:
\[ \text{side} = \sqrt{16} \]
Calculating the square root:
\[ \text{side} = 4 \, \text{cm} \]

### Step 5: Calculate the volume of the cube.
The volume (V) of a cube is given by the formula:
\[ V = \text{side}^3 \]
Substituting the side length we found:
\[ V = 4^3 \]
Calculating \(4^3\):
\[ V = 4 \times 4 \times 4 = 16 \times 4 = 64 \, \text{cm}^3 \]

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

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