A cube has a side of length 2.342m. Find volume and surface area in correct significant figures.

Explanation

To solve the problem of finding the volume and surface area of a cube with a side length of 2.342 meters, we will follow these steps:

### Step 1: Identify the side length of the cube
The side length \( a \) of the cube is given as:
\[ a = 2.342 \, \text{m} \]

### 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 \( a \):
\[ V = (2.342)^3 \]

Now, calculating \( (2.342)^3 \):
\[ V = 2.342 \times 2.342 \times 2.342 \]
\[ V \approx 12.85 \, \text{m}^3 \]

### Step 3: Determine the correct significant figures for the volume
The side length 2.342 has 4 significant figures. Therefore, the volume should also be expressed with 4 significant figures:
\[ V \approx 12.85 \, \text{m}^3 \]

### Step 4: Calculate the surface area of the cube
The formula for the surface area \( A \) of a cube is:
\[ A = 6a^2 \]

Substituting the value of \( a \):
\[ A = 6 \times (2.342)^2 \]

Now, calculating \( (2.342)^2 \):
\[ A = 6 \times (2.342 \times 2.342) \]
\[ A \approx 6 \times 5.485 \]
\[ A \approx 32.91 \, \text{m}^2 \]

### Step 5: Determine the correct significant figures for the surface area
Since the side length 2.342 has 4 significant figures, the surface area should also be expressed with 4 significant figures:
\[ A \approx 32.91 \, \text{m}^2 \]

### Final Answers
- Volume: \( 12.85 \, \text{m}^3 \)
- Surface Area: \( 32.91 \, \text{m}^2 \)