The radius of a circle is stated as 2.12 cm. Its area should be written as

Options

A. `14 cm^2`
B. `14.1 cm^2`
C. `14.11 cm^2`
D. `14.1124 cm^2`

Answer

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 is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given radius into the formula.
In this case, the radius \( r \) is given as 2.12 cm. Therefore, we can substitute this value into the formula:
\[ A = \pi (2.12)^2 \]

### Step 3: Calculate \( (2.12)^2 \).
First, we need to calculate \( (2.12)^2 \):
\[ (2.12)^2 = 2.12 \times 2.12 = 4.4944 \]

### Step 4: Multiply by \( \pi \).
Next, we multiply this result by \( \pi \). We can use \( \pi \approx \frac{22}{7} \) for our calculation:
\[ A \approx \frac{22}{7} \times 4.4944 \]

### Step 5: Perform the multiplication.
Calculating this gives:
\[ A \approx 22 \times 4.4944 / 7 \approx 99.8888 / 7 \approx 14.2706 \]

### Step 6: Round the result to the appropriate number of significant figures.
The radius 2.12 has 3 significant figures. Therefore, we should round our area to 3 significant figures. The area calculated is approximately 14.2706 cm². Rounding this to 3 significant figures gives us:
\[ A \approx 14.3 \, \text{cm}^2 \]

### Step 7: Compare with the options.
The options provided are 14 cm², 14.1 cm², 14.11 cm², and 14.1124 cm². The closest option to our rounded area of 14.3 cm² is 14.1 cm².

### Final Answer:
The area of the circle should be written as:
\[ \text{14.1 cm}^2 \]

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