The area of a semicircle is `1925 cm^2`. Calculate its perimeter (in cm).

Options

A. 360
B. 80
C. 160
D. 180

Answer

To solve the problem step by step, we will follow the given information and formulas related to the semicircle.

### Step 1: Use the formula for the area of a semicircle
The formula for the area of a semicircle is given by:
\[ \text{Area} = \frac{1}{2} \pi r^2 \]
We know that the area is \(1925 \, \text{cm}^2\). Therefore, we can set up the equation:
\[ \frac{1}{2} \pi r^2 = 1925 \]

### Step 2: Solve for \(r^2\)
To isolate \(r^2\), we first multiply both sides of the equation by 2:
\[ \pi r^2 = 1925 \times 2 \]
\[ \pi r^2 = 3850 \]
Next, we divide both sides by \(\pi\):
\[ r^2 = \frac{3850}{\pi} \]

### Step 3: Calculate \(r\)
Now, we take the square root of both sides to find \(r\):
\[ r = \sqrt{\frac{3850}{\pi}} \]
Using the approximate value of \(\pi \approx 3.14\):
\[ r = \sqrt{\frac{3850}{3.14}} \approx \sqrt{1225} = 35 \, \text{cm} \]

### Step 4: Calculate the perimeter of the semicircle
The formula for the perimeter \(P\) of a semicircle is given by:
\[ P = r\pi + 2r \]
Substituting the value of \(r\):
\[ P = 35\pi + 2 \times 35 \]
\[ P = 35\pi + 70 \]

### Step 5: Approximate the value of the perimeter
Using \(\pi \approx 3.14\):
\[ P \approx 35 \times 3.14 + 70 \]
\[ P \approx 109.9 + 70 = 179.9 \, \text{cm} \]
Rounding to the nearest whole number, we get:
\[ P \approx 180 \, \text{cm} \]

### Final Answer
The perimeter of the semicircle is approximately \(180 \, \text{cm}\).

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