The length, breadth the thickness of rectangular sheet of wood are 3.230 m, 1.49 m and 1.99 cm respectively. Give the total surface area and volume of the sheet correct to the significant figures.

Explanation

To solve the problem of finding the total surface area and volume of a rectangular sheet of wood with given dimensions, we will follow these steps:

### Step 1: Write down the given dimensions
- Length (L) = 3.230 m
- Breadth (B) = 1.49 m
- Thickness (H) = 1.99 cm (Convert this to meters: 1.99 cm = 0.0199 m)

### Step 2: Calculate the volume of the rectangular sheet
The formula for the volume (V) of a rectangular prism is:
\[ V = L \times B \times H \]

Substituting the values:
\[ V = 3.230 \, \text{m} \times 1.49 \, \text{m} \times 0.0199 \, \text{m} \]

Calculating this gives:
\[ V = 3.230 \times 1.49 \times 0.0199 = 0.0964 \, \text{m}^3 \]

### Step 3: Determine significant figures for the volume
- Length (3.230 m) has 4 significant figures.
- Breadth (1.49 m) has 3 significant figures.
- Thickness (0.0199 m) has 3 significant figures.

The result must be rounded to the least number of significant figures, which is 3. Thus:
\[ V = 0.0964 \, \text{m}^3 \rightarrow 0.0964 \, \text{m}^3 \text{ rounded to } 3 \text{ significant figures is } 0.0964 \, \text{m}^3 \]

### Step 4: Calculate the total surface area
The formula for the total surface area (A) of a rectangular prism is:
\[ A = 2(LB + BH + LH) \]

Substituting the values:
\[ A = 2 \left( (3.230 \times 1.49) + (1.49 \times 0.0199) + (3.230 \times 0.0199) \right) \]

Calculating each term:
1. \( LB = 3.230 \times 1.49 = 4.81 \)
2. \( BH = 1.49 \times 0.0199 = 0.0296 \)
3. \( LH = 3.230 \times 0.0199 = 0.0643 \)

Now, summing these:
\[ A = 2 \left( 4.81 + 0.0296 + 0.0643 \right) \]
\[ A = 2 \left( 4.9039 \right) = 9.8078 \, \text{m}^2 \]

### Step 5: Determine significant figures for the surface area
- \( LB \) has 3 significant figures.
- \( BH \) has 2 significant figures.
- \( LH \) has 3 significant figures.

The result must be rounded to the least number of significant figures, which is 2. Thus:
\[ A = 9.8078 \, \text{m}^2 \rightarrow 9.81 \, \text{m}^2 \text{ rounded to } 2 \text{ significant figures is } 9.81 \, \text{m}^2 \]

### Final Answers
- Volume = 0.0964 m³
- Total Surface Area = 9.81 m²