Find the total surface area of a cube whose volume is `64cm^(3)` ?

Options

A. 64`cm^(2)`
B. 84 `cm^(2)`
C. 16 `cm^(2)`
D. 96 `cm^(2)`

Answer

To find the total surface area of a cube whose volume is \(64 \, \text{cm}^3\), 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 side of the cube.

### Step 2: Set up the equation with the given volume
We know the volume is \(64 \, \text{cm}^3\), so we can set up the equation:
\[ A^3 = 64 \]

### Step 3: Solve for \(A\)
To find \(A\), we take the cube root of both sides:
\[ A = \sqrt[3]{64} \]
Calculating the cube root:
\[ A = 4 \, \text{cm} \]

### Step 4: Use the side length to find the total surface area
The total surface area \(S\) of a cube is given by the formula:
\[ S = 6A^2 \]
Substituting the value of \(A\):
\[ S = 6 \times (4 \, \text{cm})^2 \]

### Step 5: Calculate \(A^2\)
Calculating \(A^2\):
\[ A^2 = 4^2 = 16 \, \text{cm}^2 \]

### Step 6: Calculate the total surface area
Now substituting \(A^2\) back into the surface area formula:
\[ S = 6 \times 16 \, \text{cm}^2 = 96 \, \text{cm}^2 \]

### Final Answer
The total surface area of the cube is:
\[ \text{Total Surface Area} = 96 \, \text{cm}^2 \]

---