Find the perimeter (in cm) of semicircle of radius 28 cm.

Options

A. 288
B. 144
C. 121
D. 242

Answer

To find the perimeter of a semicircle with a radius of 28 cm, we can follow these steps:

### Step 1: Understand the components of the perimeter
The perimeter of a semicircle consists of two parts:
1. The straight line across the diameter.
2. The curved part, which is half of the circumference of the full circle.

### Step 2: Calculate the diameter
The diameter (d) of the semicircle can be calculated using the formula:
\[ d = 2r \]
where \( r \) is the radius.

Given that the radius \( r = 28 \) cm:
\[ d = 2 \times 28 = 56 \text{ cm} \]

### Step 3: Calculate the circumference of the full circle
The circumference (C) of a full circle is given by the formula:
\[ C = 2\pi r \]

For our semicircle:
\[ C = 2\pi \times 28 \]

### Step 4: Calculate the arc length of the semicircle
Since we only need the arc length for the semicircle, we take half of the full circumference:
\[ \text{Arc length} = \frac{C}{2} = \frac{2\pi \times 28}{2} = \pi \times 28 \]

### Step 5: Substitute the value of π
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Arc length} = \frac{22}{7} \times 28 \]

### Step 6: Calculate the arc length
\[ \text{Arc length} = \frac{22 \times 28}{7} \]
\[ = \frac{616}{7} = 88 \text{ cm} \]

### Step 7: Calculate the total perimeter
Now, we can find the total perimeter (P) of the semicircle by adding the diameter and the arc length:
\[ P = \text{Diameter} + \text{Arc length} \]
\[ P = 56 + 88 = 144 \text{ cm} \]

### Final Answer
The perimeter of the semicircle is **144 cm**.

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