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 semi-circle given its area, we can follow these steps:

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

### Step 2: Set up the equation
Given that the area of the semi-circle is \( 308 \, \text{cm}^2 \), we can set up the equation:
\[ \frac{1}{2} \pi r^2 = 308 \]

### Step 3: Multiply both sides by 2
To eliminate the fraction, multiply both sides of the equation by 2:
\[ \pi r^2 = 616 \]

### Step 4: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \), we can substitute this value into the equation:
\[ \frac{22}{7} r^2 = 616 \]

### Step 5: Multiply both sides by 7
To get rid of the fraction, multiply both sides by 7:
\[ 22 r^2 = 616 \times 7 \]

### Step 6: Calculate \( 616 \times 7 \)
Calculating the right side:
\[ 616 \times 7 = 4312 \]
So, we have:
\[ 22 r^2 = 4312 \]

### Step 7: Divide both sides by 22
Now, divide both sides by 22 to solve for \( r^2 \):
\[ r^2 = \frac{4312}{22} \]

### Step 8: Simplify \( \frac{4312}{22} \)
Calculating the division:
\[ r^2 = 196 \]

### Step 9: Take the square root
To find \( r \), take the square root of both sides:
\[ r = \sqrt{196} \]

### Step 10: Calculate the square root
Calculating the square root gives:
\[ r = 14 \]

### Conclusion
Thus, the radius of the semi-circle is:
\[ \text{Radius} = 14 \, \text{cm} \]

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