The area of a circle is 38.5 sq. cm. its circumference (in cm )is (use `pi=(22)/(7)`):

Options

A. 22
B. 24
C. 26
D. 32

Answer

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

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

### Step 2: Substitute the given area into the formula.
We know the area of the circle is \( 38.5 \) sq. cm. Therefore, we can set up the equation:
\[ \pi r^2 = 38.5 \]
Given that \( \pi = \frac{22}{7} \), we can substitute this value into the equation:
\[ \frac{22}{7} r^2 = 38.5 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), we first multiply both sides by \( 7 \) to eliminate the fraction:
\[ 22 r^2 = 38.5 \times 7 \]
Calculating \( 38.5 \times 7 \):
\[ 38.5 \times 7 = 269.5 \]
So, we have:
\[ 22 r^2 = 269.5 \]
Next, divide both sides by \( 22 \):
\[ r^2 = \frac{269.5}{22} \]

### Step 4: Calculate \( r^2 \).
Now, we perform the division:
\[ r^2 = 12.25 \]

### Step 5: Find \( r \) by taking the square root.
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{12.25} = 3.5 \text{ cm} \]

### Step 6: Write down the formula for the circumference of a circle.
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]

### Step 7: Substitute the value of \( r \) and \( \pi \) into the circumference formula.
Now we can substitute \( r = 3.5 \) cm and \( \pi = \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 3.5 \]

### Step 8: Simplify the expression.
Calculating \( 2 \times 3.5 = 7 \):
\[ C = \frac{22}{7} \times 7 \]
The \( 7 \) cancels out:
\[ C = 22 \text{ cm} \]

### Final Answer:
The circumference of the circle is \( 22 \) cm.