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 is \( 38.5 \, \text{sq. cm} \). Using \( \pi = \frac{22}{7} \), we can set up the equation:
\[ 38.5 = \frac{22}{7} r^2 \]

### Step 3: Convert \( 38.5 \) into a fraction for easier calculations.
We can express \( 38.5 \) as:
\[ 38.5 = \frac{385}{10} \]

### Step 4: Clear the fraction by multiplying both sides by \( 10 \).
Multiply both sides by \( 10 \) to eliminate the denominator:
\[ 385 = \frac{22}{7} r^2 \times 10 \]
This simplifies to:
\[ 385 = \frac{220}{7} r^2 \]

### Step 5: Multiply both sides by \( 7 \) to eliminate the fraction.
\[ 385 \times 7 = 220 r^2 \]
Calculating \( 385 \times 7 \):
\[ 2695 = 220 r^2 \]

### Step 6: Divide both sides by \( 220 \) to solve for \( r^2 \).
\[ r^2 = \frac{2695}{220} \]

### Step 7: Simplify \( \frac{2695}{220} \).
We can simplify this fraction:
\[ r^2 = \frac{2695 \div 5}{220 \div 5} = \frac{539}{44} \]

### Step 8: Calculate \( r \) by taking the square root.
\[ r = \sqrt{\frac{539}{44}} = \frac{\sqrt{539}}{\sqrt{44}} = \frac{\sqrt{539}}{2\sqrt{11}} \]

### Step 9: Calculate the circumference using the radius.
The circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
Substituting \( \pi = \frac{22}{7} \) and \( r = \frac{7}{2} \):
\[ C = 2 \times \frac{22}{7} \times \frac{7}{2} \]

### Step 10: Simplify the expression for circumference.
The \( 2 \) and \( \frac{7}{2} \) cancel out:
\[ C = 22 \, \text{cm} \]

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

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