The volume of a cube is `2744 cm^(3)` . Its surface area is

Options

A. `196 cm^(2)`
B. `1176cm^(2)`
C. `784 cm^(2)`
D. `588 cm^(2)`

Explanation

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

### Step 1: Understand the formula for the volume of a cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of one edge of the cube.

### Step 2: Set up the equation with the given volume.
Given that the volume of the cube is \( 2744 \, \text{cm}^3 \), we can write:
\[ a^3 = 2744 \]

### Step 3: Calculate the edge length \( a \) by taking the cube root.
To find \( a \), we need to take the cube root of both sides:
\[ a = \sqrt[3]{2744} \]

### Step 4: Calculate the cube root.
Calculating the cube root of \( 2744 \):
\[ a = 14 \, \text{cm} \]

### Step 5: Use the edge length to find the surface area.
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]

### Step 6: Substitute the value of \( a \) into the surface area formula.
Now substitute \( a = 14 \, \text{cm} \) into the surface area formula:
\[ S = 6 \times (14)^2 \]

### Step 7: Calculate \( (14)^2 \).
Calculating \( (14)^2 \):
\[ (14)^2 = 196 \]

### Step 8: Calculate the total surface area.
Now substitute back to find \( S \):
\[ S = 6 \times 196 = 1176 \, \text{cm}^2 \]

### Final Answer:
The surface area of the cube is \( 1176 \, \text{cm}^2 \).

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