The diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 36 pi sq cm.

Options

A. a. 75
B. b.144
C. c. 36
D. d. 18

Answer

To find the area of the square when the diameter of the circle is equal to the side of the square, and the area of the circle is given as 36π square centimeters, follow these steps:

### Step 1: Find the radius of the circle
The area of a circle is given by the formula:
\[ \text{Area} = \pi r^2 \]
Given that the area of the circle is \(36\pi\) square centimeters, we can set up the equation:
\[ \pi r^2 = 36\pi \]
Now, divide both sides by \(\pi\):
\[ r^2 = 36 \]
To find \(r\), take the square root of both sides:
\[ r = \sqrt{36} = 6 \text{ cm} \]

### Step 2: Calculate the diameter of the circle
The diameter \(d\) of the circle is twice the radius:
\[ d = 2r \]
Substituting the value of \(r\):
\[ d = 2 \times 6 = 12 \text{ cm} \]

### Step 3: Determine the side of the square
According to the problem, the diameter of the circle is equal to the side of the square. Therefore, the side \(s\) of the square is:
\[ s = d = 12 \text{ cm} \]

### Step 4: Calculate the area of the square
The area \(A\) of a square is given by the formula:
\[ A = s^2 \]
Substituting the value of \(s\):
\[ A = 12^2 = 144 \text{ square centimeters} \]

### Final Answer
The area of the square is \(144\) square centimeters.

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