The area of a circle is `36 pi sq. m` Find its circumference.

Options

A. `18 pi cm`
B. `12 pi cm`
C. `14 pi cm`
D. `16 pi cm`

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: Set the area equal to the given value.
We know from the problem that the area is \( 36\pi \) square meters. Therefore, we can set up the equation:
\[ \pi r^2 = 36\pi \]

### Step 3: Simplify the equation.
We can divide both sides of the equation by \( \pi \) (assuming \( \pi \neq 0 \)):
\[ r^2 = 36 \]

### Step 4: Solve for the radius \( r \).
To find \( r \), we take the square root of both sides:
\[ r = \sqrt{36} = 6 \text{ meters} \]

### Step 5: 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 6: Substitute the value of \( r \) into the circumference formula.
Now, we can substitute \( r = 6 \) meters into the circumference formula:
\[ C = 2\pi(6) \]

### Step 7: Calculate the circumference.
Now, calculate the value:
\[ C = 12\pi \text{ meters} \]

### Final Answer:
The circumference of the circle is \( 12\pi \) meters.

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