If the area of a circle is equal to the area of square with side `2 root `pi units, what is the diameter of the circle ?

Options

A. 1 unit
B. 2 units
C. 4 units
D. 8 units

Answer

To solve the problem, we need to find the diameter of a circle given that its area is equal to the area of a square with a side length of \( 2\sqrt{\pi} \) units.

### Step 1: Calculate the area of the square
The area of a square is given by the formula:
\[ \text{Area of square} = \text{side}^2 \]
Given that the side of the square is \( 2\sqrt{\pi} \), we can calculate the area:
\[ \text{Area of square} = (2\sqrt{\pi})^2 = 4\pi \]

### Step 2: Set the area of the circle equal to the area of the square
The area of a circle is given by the formula:
\[ \text{Area of circle} = \pi r^2 \]
where \( r \) is the radius of the circle. According to the problem, the area of the circle is equal to the area of the square:
\[ \pi r^2 = 4\pi \]

### Step 3: Simplify the equation
We can simplify the equation by dividing both sides by \( \pi \) (assuming \( \pi \neq 0 \)):
\[ r^2 = 4 \]

### Step 4: Solve for the radius
To find the radius \( r \), we take the square root of both sides:
\[ r = \sqrt{4} = 2 \]

### Step 5: Calculate the diameter
The diameter \( d \) of the circle is related to the radius by the formula:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 2 = 4 \]

### Final Answer
The diameter of the circle is \( 4 \) units.

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