The length , breadth , and thickness of a metal sheet are `4.234 m , 1.005 m , and 2.01 cm`, respectively. Give the area and volume of the sheet to the correct number of significant figures.

Explanation

To solve the problem of finding the area and volume of a metal sheet given its dimensions, we will follow these steps:

### Step 1: Convert all measurements to the same unit
The dimensions given are:
- Length (L) = 4.234 m
- Breadth (B) = 1.005 m
- Thickness (T) = 2.01 cm

First, we need to convert the thickness from centimeters to meters:
\[ T = 2.01 \, \text{cm} = \frac{2.01}{100} \, \text{m} = 0.0201 \, \text{m} \]

### Step 2: Calculate the area of the sheet
The area of the metal sheet consists of the areas of its six surfaces. The formula for the total surface area (A) is:
\[ A = 2(L \times B + B \times T + T \times L) \]

Substituting the values:
\[ A = 2(4.234 \times 1.005 + 1.005 \times 0.0201 + 0.0201 \times 4.234) \]

Calculating each term:
1. \(4.234 \times 1.005 = 4.26017\)
2. \(1.005 \times 0.0201 = 0.020201\)
3. \(0.0201 \times 4.234 = 0.0850284\)

Now summing these:
\[ A = 2(4.26017 + 0.020201 + 0.0850284) = 2(4.3653994) = 8.7307988 \, \text{m}^2 \]

### Step 3: Round the area to the correct number of significant figures
The least number of significant figures among the measurements is 3 (from 2.01 cm). Therefore, we round the area:
\[ A \approx 8.73 \, \text{m}^2 \]

### Step 4: Calculate the volume of the sheet
The volume (V) of the metal sheet is given by:
\[ V = L \times B \times T \]

Substituting the values:
\[ V = 4.234 \times 1.005 \times 0.0201 \]

Calculating:
1. \(4.234 \times 1.005 = 4.26017\)
2. \(4.26017 \times 0.0201 = 0.0855289 \, \text{m}^3\)

### Step 5: Round the volume to the correct number of significant figures
Again, the least number of significant figures is 3. Therefore, we round the volume:
\[ V \approx 0.0855 \, \text{m}^3 \]

### Final Answers:
- Area = \(8.73 \, \text{m}^2\)
- Volume = \(0.0855 \, \text{m}^3\)

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