The diameter of a circle is 2.486 m. Calculate the area with due regard to significant figures.

Options

A. `4.85 m^3`
B. `4.85454 m^3`
C. `4.854 m^3`
D. `4.8545 m^3`

Explanation

To calculate the area of a circle given its diameter, we can follow these steps:

### Step 1: Identify the diameter
The given diameter of the circle is 2.486 m.

### Step 2: Calculate the radius
The radius (r) of the circle is half of the diameter.

\[ r = \frac{d}{2} = \frac{2.486 \, \text{m}}{2} = 1.243 \, \text{m} \]

### Step 3: Use the formula for the area of a circle
The area (A) of a circle is calculated using the formula:

\[ A = \pi r^2 \]

### Step 4: Substitute the radius into the area formula
Now we will substitute the radius we calculated into the area formula:

\[ A = \pi (1.243 \, \text{m})^2 \]

### Step 5: Calculate the area
Calculating \( (1.243 \, \text{m})^2 \):

\[ (1.243 \, \text{m})^2 = 1.545649 \, \text{m}^2 \]

Now, multiplying by \(\pi\):

\[ A \approx 3.14159 \times 1.545649 \, \text{m}^2 \approx 4.855 \, \text{m}^2 \]

### Step 6: Determine significant figures
The diameter 2.486 m has four significant figures. Therefore, we should express the area with four significant figures as well.

Thus, the area of the circle, rounded to four significant figures, is:

\[ A \approx 4.855 \, \text{m}^2 \]

### Final Answer
The area of the circle is approximately **4.855 m²**.

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