What would be the area of a circle whose circumference is 35.2 cms ?

Options

A. 67.22 sq. cms
B. 75.54 sq. cms
C. 98.56 sq. cms
D. 86.75 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
We know the circumference is 35.2 cm. So, we can set up the equation:
\[ 2\pi r = 35.2 \]

### 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 \( C \):
\[ r = \frac{35.2}{2\pi} \]

Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{35.2}{2 \times \frac{22}{7}} \]
\[ r = \frac{35.2 \times 7}{2 \times 22} \]
\[ r = \frac{246.4}{44} \]
\[ r = 5.6 \text{ cm} \]

### 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:
\[ A = \pi (5.6)^2 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (5.6 \times 5.6) \]

### Step 6: Calculate \( 5.6 \times 5.6 \)
Calculating \( 5.6 \times 5.6 \):
\[ 5.6 \times 5.6 = 31.36 \]

### Step 7: Substitute back into the area formula
Now substitute this back into the area formula:
\[ A = \frac{22}{7} \times 31.36 \]

### Step 8: Perform the multiplication
Calculating the area:
\[ A = \frac{22 \times 31.36}{7} \]
\[ A = \frac{690.92}{7} \]
\[ A = 98.56 \text{ cm}^2 \]

### Final Answer
Thus, the area of the circle is:
\[ \text{Area} = 98.56 \text{ cm}^2 \]

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