The ratio between the area of a square and that of a circle, when the length of a side of the square is equal to that of the diameter of the circle, is
(Take, `pi = (22)/(7)`)

Options

A. `14:11`
B. `28:11`
C. `7:22`
D. `22:7`

Answer

To find the ratio between the area of a square and that of a circle when the length of a side of the square is equal to the diameter of the circle, we can follow these steps:

### Step 1: Define the side length of the square
Let the length of a side of the square be \( A \). Since the diameter of the circle is equal to the side of the square, we also have:
- Diameter of the circle = \( A \)

### Step 2: Calculate the radius of the circle
The radius \( r \) of the circle can be calculated as:
\[ r = \frac{\text{Diameter}}{2} = \frac{A}{2} \]

### Step 3: Calculate the area of the square
The area \( A_s \) of the square is given by:
\[ A_s = \text{side}^2 = A^2 \]

### Step 4: Calculate the area of the circle
The area \( A_c \) of the circle is given by the formula:
\[ A_c = \pi r^2 \]
Substituting the value of \( r \):
\[ A_c = \pi \left(\frac{A}{2}\right)^2 = \pi \cdot \frac{A^2}{4} = \frac{\pi A^2}{4} \]

### Step 5: Find the ratio of the areas
Now, we need to find the ratio of the area of the square to the area of the circle:
\[ \text{Ratio} = \frac{A_s}{A_c} = \frac{A^2}{\frac{\pi A^2}{4}} = \frac{A^2 \cdot 4}{\pi A^2} \]
The \( A^2 \) terms cancel out:
\[ \text{Ratio} = \frac{4}{\pi} \]

### Step 6: Substitute the value of \( \pi \)
Given \( \pi = \frac{22}{7} \), we substitute this value into the ratio:
\[ \text{Ratio} = \frac{4}{\frac{22}{7}} = 4 \cdot \frac{7}{22} = \frac{28}{22} \]

### Step 7: Simplify the ratio
Now, we can simplify \( \frac{28}{22} \):
\[ \frac{28}{22} = \frac{14}{11} \]

### Final Answer
Thus, the ratio between the area of the square and the area of the circle is:
\[ \text{Ratio} = 14 : 11 \]

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