Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m. (Take `sqrt3 = 1.73`)

Answer

To solve the problem of finding the volume, lateral surface area, total surface area, and diagonal of a cube with edges measuring 9 m, we will follow these steps:

### Step 1: Calculate the Volume of the Cube
The formula for the volume \( V \) of a cube is given by:
\[ V = A^3 \]
where \( A \) is the length of an edge of the cube.

Given \( A = 9 \) m, we calculate:
\[ V = 9^3 = 9 \times 9 \times 9 = 729 \, \text{m}^3 \]

### Step 2: Calculate the Lateral Surface Area of the Cube
The formula for the lateral surface area \( L \) of a cube is:
\[ L = 4A^2 \]

Using \( A = 9 \) m, we find:
\[ L = 4 \times 9^2 = 4 \times 81 = 324 \, \text{m}^2 \]

### Step 3: Calculate the Total Surface Area of the Cube
The formula for the total surface area \( T \) of a cube is:
\[ T = 6A^2 \]

Again, using \( A = 9 \) m, we calculate:
\[ T = 6 \times 9^2 = 6 \times 81 = 486 \, \text{m}^2 \]

### Step 4: Calculate the Diagonal of the Cube
The formula for the diagonal \( D \) of a cube is:
\[ D = A \sqrt{3} \]

Given that \( \sqrt{3} \approx 1.73 \) and \( A = 9 \) m, we compute:
\[ D = 9 \times 1.73 = 15.57 \, \text{m} \]

### Summary of Results
- Volume of the cube: \( 729 \, \text{m}^3 \)
- Lateral Surface Area: \( 324 \, \text{m}^2 \)
- Total Surface Area: \( 486 \, \text{m}^2 \)
- Diagonal of the cube: \( 15.57 \, \text{m} \)

---