Find the volume and total surface area of a cube whose each edge is:
8 cm

Answer

To find the volume and total surface area of a cube with each edge measuring 8 cm, we can follow these steps:

### Step 1: Identify the length of the edge of the cube.
The length of each edge of the cube is given as 8 cm.

### Step 2: Calculate the volume of the cube.
The formula for the volume \( V \) of a cube is given by:
\[ V = \text{side}^3 \]
Substituting the value of the side:
\[ V = 8^3 = 8 \times 8 \times 8 \]
Calculating this step-by-step:
- First, calculate \( 8 \times 8 = 64 \).
- Next, multiply \( 64 \times 8 = 512 \).

Thus, the volume of the cube is:
\[ V = 512 \, \text{cm}^3 \]

### Step 3: Calculate the total surface area of the cube.
The formula for the total surface area \( A \) of a cube is given by:
\[ A = 6 \times \text{side}^2 \]
Substituting the value of the side:
\[ A = 6 \times 8^2 \]
Calculating \( 8^2 \):
\[ 8^2 = 64 \]
Now substituting back into the surface area formula:
\[ A = 6 \times 64 \]
Calculating this:
- Multiply \( 6 \times 64 = 384 \).

Thus, the total surface area of the cube is:
\[ A = 384 \, \text{cm}^2 \]

### Final Results:
- Volume of the cube: \( 512 \, \text{cm}^3 \)
- Total surface area of the cube: \( 384 \, \text{cm}^2 \)

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