If the radius of a circle with area `154cm^(2)` is equal to the side of a square. Then, the area of the square is

Options

A. `47cm^(2)`
B. `49cm^(2)`
C. `48cm^(2)`
D. `54cm^(2)`

Answer

To solve the problem, we need to find the area of a square given that the radius of a circle with an area of 154 cm² is equal to the side of the square.

### Step-by-Step Solution:

1. **Understand the area of the circle**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

2. **Set up the equation**:
We know the area of the circle is 154 cm². Therefore, we can write:
\[ \pi r^2 = 154 \]

3. **Solve for \( r^2 \)**:
To find \( r^2 \), we can rearrange the equation:
\[ r^2 = \frac{154}{\pi} \]

4. **Calculate \( r^2 \)**:
Using the approximate value of \( \pi \approx 3.14 \):
\[ r^2 = \frac{154}{3.14} \approx 49.04 \]

5. **Find \( r \)**:
To find the radius \( r \), we take the square root of \( r^2 \):
\[ r \approx \sqrt{49.04} \approx 7 \text{ cm} \]

6. **Determine the area of the square**:
Since the radius of the circle is equal to the side of the square, the side of the square \( s \) is also 7 cm. The area \( A_s \) of the square is given by:
\[ A_s = s^2 = 7^2 = 49 \text{ cm}^2 \]

### Final Answer:
The area of the square is \( 49 \text{ cm}^2 \).

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