The total surface area of a cube is `1176 cm^(2)`. What is the volume of this cube ?

Options

A. a)`2744 cm^(3)`
B. b)`2644 cm^(3)`
C. c)`2544 cm^(3)`
D. d)`2844 cm^(3)`

Answer

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:
\[ \text{TSA} = 6a^2 \]
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 that the total surface area of the cube is \( 1176 \, \text{cm}^2 \). Thus, we can set up the equation:
\[ 6a^2 = 1176 \]

### Step 3: Solve for \( a^2 \).
To isolate \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{1176}{6} \]
Calculating the right side:
\[ a^2 = 196 \]

### Step 4: Solve for \( a \).
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{196} \]
Calculating the square root:
\[ a = 14 \, \text{cm} \]

### 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 \( a \):
\[ V = 14^3 \]
Calculating \( 14^3 \):
\[ V = 14 \times 14 \times 14 = 196 \times 14 = 2744 \, \text{cm}^3 \]

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

---