The length and breadth of a metal sheet are 3.124m and 3.002m respectively. The area of this sheet upto correct significant figure is

Options

A. `9.378 m^(2)`
B. `9.37 m^(2)`
C. `9.378248 m^2`
D. `9.3782 m^2`

Answer

To find the area of a metal sheet given its length and breadth, we can follow these steps:

### Step 1: Identify the Length and Breadth
The length (L) of the metal sheet is given as:
\[ L = 3.124 \, \text{m} \]

The breadth (B) of the metal sheet is given as:
\[ B = 3.002 \, \text{m} \]

### Step 2: Calculate the Area
The area (A) of a rectangle is calculated using the formula:
\[ A = L \times B \]

Substituting the values:
\[ A = 3.124 \, \text{m} \times 3.002 \, \text{m} \]

### Step 3: Perform the Multiplication
Now, we perform the multiplication:
\[ A = 3.124 \times 3.002 = 9.378248 \, \text{m}^2 \]

### Step 4: Determine Significant Figures
Next, we need to round the area to the correct number of significant figures.

- The length (3.124 m) has **4 significant figures**.
- The breadth (3.002 m) also has **4 significant figures**.

When multiplying, the result should have the same number of significant figures as the measurement with the least number of significant figures. In this case, both measurements have 4 significant figures.

### Step 5: Round the Area
Now we round the calculated area (9.378248 m²) to 4 significant figures:
\[ A \approx 9.378 \, \text{m}^2 \]

### Final Answer
Thus, the area of the metal sheet, rounded to the correct significant figures, is:
\[ \boxed{9.378 \, \text{m}^2} \]

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