If the volume of a cube is `125 cm^(3)` , then its surface area is

Options

A. `150 cm ^(2) `
B. ` 125 cm ^(2)`
C. ` 100 cm ^(2)`
D. none of these

Answer

To find the surface area of a cube when the volume is given, 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 the volume equal to the given value.
We know from the problem that the volume of the cube is \( 125 \, \text{cm}^3 \):
\[ a^3 = 125 \]

### Step 3: Solve for \( a \).
To find \( a \), we need to take the cube root of both sides:
\[ a = \sqrt[3]{125} \]
Since \( 125 = 5^3 \), we have:
\[ a = 5 \, \text{cm} \]

### Step 4: Use the formula for the surface area of a cube.
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]

### Step 5: Substitute the value of \( a \) into the surface area formula.
Now, substituting \( a = 5 \, \text{cm} \) into the surface area formula:
\[ S = 6 \times (5)^2 \]

### Step 6: Calculate \( (5)^2 \).
Calculating \( (5)^2 \):
\[ (5)^2 = 25 \]

### Step 7: Multiply by 6 to find the surface area.
Now, we multiply by 6:
\[ S = 6 \times 25 = 150 \, \text{cm}^2 \]

### Final Answer:
The surface area of the cube is \( 150 \, \text{cm}^2 \).

---