The area of a semicircle is 308 `cm^(2) .` Calculate its perimeter (in cm).

Options

A. 144
B. 49
C. 98
D. 72

Answer

To solve the problem, we need to find the perimeter of a semicircle given its area. Here’s a step-by-step solution:

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

### Step 2: Set up the equation
Given that the area of the semicircle is 308 cm², we can set up the equation:
\[ \frac{1}{2} \pi r^2 = 308 \]

### Step 3: Solve for \( r^2 \)
To isolate \( r^2 \), we first multiply both sides by 2:
\[ \pi r^2 = 616 \]
Next, we divide both sides by \( \pi \):
\[ r^2 = \frac{616}{\pi} \]

### Step 4: Substitute the value of \( \pi \)
Using \( \pi \approx 3.14 \):
\[ r^2 = \frac{616}{3.14} \approx 196 \]

### Step 5: Calculate \( r \)
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{196} = 14 \text{ cm} \]

### Step 6: Calculate the perimeter of the semicircle
The perimeter \( P \) of a semicircle is given by the formula:
\[ P = \pi r + 2r \]
Substituting the value of \( r \):
\[ P = \pi \times 14 + 2 \times 14 \]

### Step 7: Calculate \( \pi \times 14 \)
Using \( \pi \approx 3.14 \):
\[ P = 3.14 \times 14 + 28 \]
Calculating \( 3.14 \times 14 \):
\[ 3.14 \times 14 \approx 43.96 \]

### Step 8: Add the values
Now, we add \( 43.96 + 28 \):
\[ P \approx 43.96 + 28 = 71.96 \text{ cm} \]
Rounding this to the nearest whole number, we get:
\[ P \approx 72 \text{ cm} \]

### Final Answer
The perimeter of the semicircle is approximately **72 cm**.

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