Find the volume, laterial surface area and the total surface area of a cube each of whose sides measures 8 cm.

Answer

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

### Step 1: Identify the side length of the cube
Given:
- Side length (a) = 8 cm

### Step 2: Calculate the Volume of the Cube
The formula for the volume (V) of a cube is:
\[ V = a^3 \]
Substituting the value of a:
\[ V = 8^3 \]
Calculating \( 8^3 \):
\[ V = 8 \times 8 \times 8 = 512 \, \text{cm}^3 \]

### Step 3: Calculate the Lateral Surface Area of the Cube
The formula for the lateral surface area (LSA) of a cube is:
\[ \text{LSA} = 4a^2 \]
Substituting the value of a:
\[ \text{LSA} = 4 \times (8^2) \]
Calculating \( 8^2 \):
\[ \text{LSA} = 4 \times 64 = 256 \, \text{cm}^2 \]

### Step 4: Calculate the Total Surface Area of the Cube
The formula for the total surface area (TSA) of a cube is:
\[ \text{TSA} = 6a^2 \]
Substituting the value of a:
\[ \text{TSA} = 6 \times (8^2) \]
Calculating \( 8^2 \):
\[ \text{TSA} = 6 \times 64 = 384 \, \text{cm}^2 \]

### Final Results
- Volume of the cube: \( 512 \, \text{cm}^3 \)
- Lateral Surface Area of the cube: \( 256 \, \text{cm}^2 \)
- Total Surface Area of the cube: \( 384 \, \text{cm}^2 \)

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