If the volume of a cube is `1728 cm^(3)` then what is the total surface area (in `cm^(2)`) of the cube ?

Options

A. 144
B. 288
C. 276
D. 864

Answer

To find the total 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 can be calculated using the formula:
\[ V = a^3 \]
where \( a \) is the length of a side of the cube.

### Step 2: Set up the equation using the given volume
We are given that the volume of the cube is \( 1728 \, \text{cm}^3 \). Therefore, we can set up the equation:
\[ a^3 = 1728 \]

### Step 3: Solve for the side length \( a \)
To find \( a \), we need to take the cube root of \( 1728 \):
\[ a = \sqrt[3]{1728} \]
Calculating the cube root:
\[ a = 12 \, \text{cm} \]

### Step 4: Use the side length to find the total surface area
The total surface area \( A \) of a cube can be calculated using the formula:
\[ A = 6a^2 \]
Now substituting the value of \( a \):
\[ A = 6 \times (12 \, \text{cm})^2 \]

### Step 5: Calculate \( A \)
First, calculate \( (12 \, \text{cm})^2 \):
\[ (12 \, \text{cm})^2 = 144 \, \text{cm}^2 \]
Now substitute this value back into the surface area formula:
\[ A = 6 \times 144 \, \text{cm}^2 = 864 \, \text{cm}^2 \]

### Final Answer
The total surface area of the cube is \( 864 \, \text{cm}^2 \).

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