The area of a circle is `324 pi` square cm. The length of its longest chord (in cm.) is

Options

A. 36
B. 28
C. 38
D. 32

Answer

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

### Step 1: Understand 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 up the equation with the given area.
We know that the area of the circle is \( 324 \pi \) square cm. Therefore, we can set up the equation:
\[ \pi r^2 = 324 \pi \]

### Step 3: Simplify the equation.
To simplify, we can divide both sides of the equation by \( \pi \):
\[ r^2 = 324 \]

### Step 4: Solve for the radius.
Now, take the square root of both sides to find the radius \( r \):
\[ r = \sqrt{324} = 18 \text{ cm} \]

### Step 5: Find the diameter of the circle.
The diameter \( d \) of the circle is twice the radius:
\[ d = 2r = 2 \times 18 = 36 \text{ cm} \]

### Step 6: State the length of the longest chord.
The longest chord of a circle is the diameter. Therefore, the length of the longest chord is:
\[ \text{Length of the longest chord} = 36 \text{ cm} \]

### Final Answer:
The length of the longest chord is **36 cm**.

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