The cicrcumference of a circle is give by the formula `C = pid` where d is the diameter of the circle. The formula for the area of a circle is `A = pir^2`. If the area of the circle is `9pi`, what is the circumference of the circle ?

Options

A. `9pi`
B. 9
C. `6pi`
D. 6

Answer

To find the circumference of the circle given that its area is \(9\pi\), we can follow these steps:

### Step 1: Use the area formula
The area \(A\) of a circle is given by the formula:
\[ A = \pi r^2 \]
Given that the area is \(9\pi\), we can set up the equation:
\[ \pi r^2 = 9\pi \]

### Step 2: Simplify the equation
We can divide both sides of the equation by \(\pi\) (assuming \(\pi \neq 0\)):
\[ r^2 = 9 \]

### Step 3: Solve for the radius
To find \(r\), we take the square root of both sides:
\[ r = \sqrt{9} \]
This gives us:
\[ r = 3 \]
Since the radius cannot be negative, we take the positive value.

### Step 4: Calculate the diameter
The diameter \(d\) of the circle is twice the radius:
\[ d = 2r = 2 \times 3 = 6 \]

### Step 5: Use the circumference formula
The circumference \(C\) of a circle is given by the formula:
\[ C = \pi d \]
Substituting the value of \(d\):
\[ C = \pi \times 6 = 6\pi \]

### Final Answer
Thus, the circumference of the circle is:
\[ C = 6\pi \]

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