Find the surface area and the volume of a cube of an edge :
12 cm

Answer

To find the surface area and volume of a cube with an edge length of 12 cm, we will follow these steps:

### Step 1: Understand the formulas
The surface area \( A \) of a cube is given by the formula:
\[ A = 6a^2 \]
where \( a \) is the length of an edge of the cube.

The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]

### Step 2: Substitute the edge length into the surface area formula
Given that the edge length \( a = 12 \) cm, we can substitute this value into the surface area formula:
\[ A = 6 \times (12)^2 \]

### Step 3: Calculate \( (12)^2 \)
First, we calculate \( (12)^2 \):
\[ (12)^2 = 144 \]

### Step 4: Calculate the surface area
Now substitute \( 144 \) back into the surface area formula:
\[ A = 6 \times 144 \]
Calculating this gives:
\[ A = 864 \text{ cm}^2 \]

### Step 5: Substitute the edge length into the volume formula
Now we will calculate the volume using the edge length:
\[ V = (12)^3 \]

### Step 6: Calculate \( (12)^3 \)
First, we calculate \( (12)^3 \):
\[ (12)^3 = 12 \times 12 \times 12 \]
Calculating \( 12 \times 12 = 144 \), then multiplying by \( 12 \):
\[ 144 \times 12 = 1728 \]

### Step 7: State the volume
Thus, the volume of the cube is:
\[ V = 1728 \text{ cm}^3 \]

### Final Answers
- Surface Area: \( 864 \text{ cm}^2 \)
- Volume: \( 1728 \text{ cm}^3 \)

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