The volume of a cube is 64 `cm^3`. Its surface area is

Options

A. `16cm^2`
B. `64cm^2`
C. `96cm^2`
D. `128cm^2`

Answer

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

### Step-by-Step Solution:

1. **Understand 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.

2. **Set Up the Equation**:
Given that the volume of the cube is \( 64 \, \text{cm}^3 \), we can write:
\[ a^3 = 64 \]

3. **Find the Length of One Side**:
To find \( a \), we need to take the cube root of both sides:
\[ a = \sqrt[3]{64} \]
Since \( 64 = 4 \times 4 \times 4 \), we find:
\[ a = 4 \, \text{cm} \]

4. **Calculate the Surface Area**:
The surface area \( SA \) of a cube is given by the formula:
\[ SA = 6a^2 \]
Now, substituting \( a = 4 \, \text{cm} \):
\[ SA = 6 \times (4)^2 \]

5. **Simplify the Calculation**:
Calculate \( (4)^2 \):
\[ (4)^2 = 16 \]
Now, substitute back into the surface area formula:
\[ SA = 6 \times 16 \]

6. **Final Calculation**:
Multiply to find the surface area:
\[ SA = 96 \, \text{cm}^2 \]

### Final Answer:
The surface area of the cube is \( 96 \, \text{cm}^2 \).

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