The radius of a disc is 1.2 cm. Its area according to idea of significant figures, will be given by :-

Options

A. `14.1124 m^(2)`
B. `14.112 m^(2)`
C. `14.11 m^(2)`
D. `14.1 m^(2)`

Answer

To find the area of a disc with a radius of 1.2 cm while considering significant figures, we can follow these steps:

### Step 1: Identify the formula for the area of a disc.
The area \( A \) of a disc is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the disc.

### Step 2: Substitute the given radius into the formula.
Given that the radius \( r = 1.2 \) cm, we can substitute this value into the formula:
\[ A = \pi (1.2)^2 \]

### Step 3: Calculate \( (1.2)^2 \).
Calculating the square of the radius:
\[ (1.2)^2 = 1.44 \]

### Step 4: Multiply by \( \pi \).
Using \( \pi \approx \frac{22}{7} \) for the calculation, we have:
\[ A \approx \frac{22}{7} \times 1.44 \]
Calculating this gives:
\[ A \approx 4.523 \text{ cm}^2 \]

### Step 5: Apply significant figures.
The radius \( 1.2 \) cm has 2 significant figures. According to the rules of significant figures, the result should also be reported with 2 significant figures.

### Step 6: Round the result to 2 significant figures.
The calculated area \( 4.523 \) cm² rounded to 2 significant figures is:
\[ 4.5 \text{ cm}^2 \]

### Final Answer:
The area of the disc is \( 4.5 \text{ cm}^2 \).

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