What would be the area of a circle whose diameter is 30.8 cm?

Options

A. 762.28 sq cm
B. 775.15 sq cm
C. 745.36 sq cm
D. 722.14 sq cm

Explanation

To find the area of a circle when the diameter is given, we can follow these steps:

### Step 1: Identify the diameter
The diameter of the circle is given as 30.8 cm.

### Step 2: Calculate the radius
The radius (r) of a circle is half of the diameter. Therefore, we can calculate the radius as follows:
\[ r = \frac{d}{2} = \frac{30.8 \, \text{cm}}{2} = 15.4 \, \text{cm} \]

### Step 3: Use the area formula
The area (A) of a circle can be calculated using the formula:
\[ A = \pi r^2 \]
We will use \(\pi \approx \frac{22}{7}\) for our calculations.

### Step 4: Substitute the radius into the area formula
Now we substitute the radius into the area formula:
\[ A = \frac{22}{7} \times (15.4)^2 \]

### Step 5: Calculate \( (15.4)^2 \)
Calculating \( (15.4)^2 \):
\[ (15.4)^2 = 237.16 \]

### Step 6: Substitute back into the area formula
Now substitute \( (15.4)^2 \) back into the area formula:
\[ A = \frac{22}{7} \times 237.16 \]

### Step 7: Perform the multiplication
Calculating the area:
\[ A = \frac{22 \times 237.16}{7} = \frac{5217.52}{7} \approx 745.36 \, \text{cm}^2 \]

### Final Answer
Thus, the area of the circle is approximately \( 745.36 \, \text{cm}^2 \).

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