The circumference of a circle is 56 cm. Find the approximate area of square if the radius is two times of the side of a square.

Options

A. `18 cm^2`
B. `32 cm^2`
C. `25 cm^2`
D. `20cm^2`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Find the radius of the circle
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
Given that the circumference is 56 cm, we can set up the equation:
\[ 2\pi r = 56 \]
To find the radius \( r \), we rearrange the equation:
\[ r = \frac{56}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{56}{2 \times \frac{22}{7}} = \frac{56 \times 7}{44} = \frac{392}{44} = \frac{98}{11} \text{ cm} \]

### Step 2: Relate the radius to the side of the square
According to the problem, the radius \( r \) is two times the side \( s \) of the square:
\[ r = 2s \]
Substituting the value of \( r \):
\[ \frac{98}{11} = 2s \]
To find the side \( s \):
\[ s = \frac{98}{11 \times 2} = \frac{98}{22} = \frac{49}{11} \text{ cm} \]

### Step 3: Calculate the area of the square
The area \( A \) of a square is given by:
\[ A = s^2 \]
Substituting the value of \( s \):
\[ A = \left(\frac{49}{11}\right)^2 = \frac{49^2}{11^2} = \frac{2401}{121} \text{ cm}^2 \]

### Step 4: Approximate the area
To approximate the area, we can divide:
\[ \frac{2401}{121} \approx 19.83 \text{ cm}^2 \]
Rounding this gives us approximately:
\[ A \approx 20 \text{ cm}^2 \]

### Final Answer
The approximate area of the square is \( 20 \text{ cm}^2 \).

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