If the circumference of a circle is 44 cm., then must be its area (in `cm^(2)`) ?

Options

A. 308
B. 240
C. 154
D. 480

Answer

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

### Step 1: Write down the formula for circumference
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given circumference
We know the circumference is 44 cm. Therefore, we can set up the equation:
\[ 2\pi r = 44 \]

### Step 3: Solve for the radius \( r \)
To find the radius, we can rearrange the equation:
\[ r = \frac{44}{2\pi} \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ r = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7 \text{ cm} \]

### Step 4: Write down the formula for area
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]

### Step 5: Substitute the radius into the area formula
Now we can substitute the radius we found into the area formula:
\[ A = \pi (7)^2 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ A = \frac{22}{7} \times 49 \]

### Step 6: Calculate the area
Now, we can simplify:
\[ A = \frac{22 \times 49}{7} = 22 \times 7 = 154 \text{ cm}^2 \]

### Final Answer
Thus, the area of the circle is:
\[ \boxed{154 \text{ cm}^2} \]

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