What would be the area of a circle whose circumference is 22 cms. ?

Options

A. 34.25 sq cms.
B. 38.5 sq. cms
C. 37.6 sq. cms
D. 36.75 sq. cms

Answer

To find the area of a circle given its circumference, 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 into the formula
We know that the circumference is 22 cm, so we can set up the equation:
\[ 22 = 2\pi r \]

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

### Step 4: Write down the formula for the area of a circle
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:
\[ A = \pi \left(\frac{7}{2}\right)^2 \]
\[ A = \pi \times \frac{49}{4} \]

### Step 6: Calculate the area using \( \pi \approx \frac{22}{7} \)
Substituting \( \pi \) into the equation:
\[ A = \frac{22}{7} \times \frac{49}{4} \]
\[ A = \frac{22 \times 49}{7 \times 4} \]
\[ A = \frac{1078}{28} \]
\[ A = 38.5 \text{ cm}^2 \]

### Final Answer
The area of the circle is \( 38.5 \text{ cm}^2 \).

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