If the area of a semi-circle is `"308 cm"^2,` then find its radius (in cm).

Options

A. 28
B. 10
C. 20
D. 14

Answer

To find the radius of a semicircle given its area, we can follow these steps:

### Step 1: Understand the formula for the area of a semicircle
The formula for the area \( A \) of a semicircle is given by:
\[ A = \frac{\pi r^2}{2} \]
where \( r \) is the radius of the semicircle.

### Step 2: Set up the equation
We know the area of the semicircle is \( 308 \, \text{cm}^2 \). We can set up the equation:
\[ \frac{\pi r^2}{2} = 308 \]

### Step 3: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \), we substitute this value into the equation:
\[ \frac{\frac{22}{7} r^2}{2} = 308 \]

### Step 4: Simplify the equation
To simplify, multiply both sides by 2:
\[ \frac{22}{7} r^2 = 616 \]

### Step 5: Multiply both sides by \( \frac{7}{22} \)
Next, we multiply both sides by \( \frac{7}{22} \) to isolate \( r^2 \):
\[ r^2 = 616 \times \frac{7}{22} \]

### Step 6: Calculate the right side
Calculating \( 616 \times \frac{7}{22} \):
1. First, simplify \( \frac{616}{22} = 28 \) (since \( 616 \div 22 = 28 \)).
2. Now multiply by 7:
\[ r^2 = 28 \times 7 = 196 \]

### Step 7: Take the square root
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{196} = 14 \]

### Conclusion
Thus, the radius of the semicircle is:
\[ \boxed{14 \, \text{cm}} \]