The total surface area of a cube is `1176 cm^(2)`. Find its volume

Explanation

To solve the problem, we will 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 that the total surface area of the cube is \(1176 \, \text{cm}^2\). Therefore, we can set up the equation:
\[ 6 \times \text{side}^2 = 1176 \]

### 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:
\[ \text{side}^2 = \frac{1176}{6} \]
Calculating the right side:
\[ \text{side}^2 = 196 \]

### Step 4: Find the side length by taking the square root.
Now, we take the square root of both sides to find the side length:
\[ \text{side} = \sqrt{196} = 14 \, \text{cm} \]

### 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 value of the side:
\[ V = 14^3 \]
Calculating \(14^3\):
\[ V = 14 \times 14 \times 14 = 2744 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \(2744 \, \text{cm}^3\).

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