Radius of a circle is 2.23m. Area of the circle is

Options

A. `15.6 m^(2)`
B. `15.6149 m^(2)`
C. `15.615 m^(2)`
D. `15.62 m^(2)`

Explanation

To find the area of a circle given its radius, we can follow these steps:

### Step 1: Identify the formula for the area of a circle.
The area \( A \) of a circle can be calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given radius into the formula.
Given that the radius \( r = 2.23 \, \text{m} \), we can substitute this value into the formula:
\[ A = \pi (2.23)^2 \]

### Step 3: Calculate \( (2.23)^2 \).
Calculating the square of the radius:
\[ (2.23)^2 = 4.9729 \]

### Step 4: Multiply by \( \pi \).
Using the approximate value of \( \pi \approx 3.14 \):
\[ A = 3.14 \times 4.9729 \approx 15.6149 \, \text{m}^2 \]

### Step 5: Determine the significant figures.
The radius \( 2.23 \, \text{m} \) has three significant figures. Therefore, we need to round our area result \( 15.6149 \, \text{m}^2 \) to three significant figures.

### Step 6: Round the area to three significant figures.
Looking at \( 15.6149 \):
- The first three significant figures are \( 15.6 \).
- The next digit is \( 1 \), which means we do not round up.
Thus, the area rounded to three significant figures is:
\[ A \approx 15.6 \, \text{m}^2 \]

### Final Answer:
The area of the circle is \( 15.6 \, \text{m}^2 \).

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