The area of a circle is `616 cm^(2)`. Find its radius (in cm).

Options

A. 14
B. 28
C. 11
D. 22

Answer

To find the radius of a circle given its area, we can use the formula for the area of a circle:

\[ \text{Area} = \pi r^2 \]

Where:
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \) or \( 3.14 \)
- \( r \) is the radius of the circle

Given that the area of the circle is \( 616 \, \text{cm}^2 \), we can set up the equation:

\[ \pi r^2 = 616 \]

### Step-by-Step Solution:

1. **Substitute the value of \( \pi \)**:
\[ \frac{22}{7} r^2 = 616 \]

2. **Multiply both sides by 7 to eliminate the fraction**:
\[ 22 r^2 = 616 \times 7 \]

3. **Calculate \( 616 \times 7 \)**:
\[ 616 \times 7 = 4312 \]
So the equation becomes:
\[ 22 r^2 = 4312 \]

4. **Divide both sides by 22 to solve for \( r^2 \)**:
\[ r^2 = \frac{4312}{22} \]

5. **Calculate \( \frac{4312}{22} \)**:
\[ \frac{4312}{22} = 196 \]
Now, we have:
\[ r^2 = 196 \]

6. **Take the square root of both sides to find \( r \)**:
\[ r = \sqrt{196} \]

7. **Calculate \( \sqrt{196} \)**:
\[ r = 14 \]

### Final Answer:
The radius of the circle is \( 14 \, \text{cm} \).