What is the perimeter of a semi-circle with radius r?

Options

A. `2pir`
B. `2pir+1`
C. `pir+2r`
D. `2pir+2r`

Answer

To find the perimeter of a semi-circle with radius \( r \), we can follow these steps:

### Step 1: Understand the Components of the Semi-Circle
A semi-circle consists of two parts:
1. The curved part (which is half of the circumference of a full circle).
2. The straight part (which is the diameter of the circle).

### Step 2: Calculate the Curved Length
The circumference of a full circle is given by the formula:
\[ C = 2\pi r \]
Since a semi-circle is half of a full circle, the length of the curved part is:
\[ \text{Curved Length} = \frac{C}{2} = \frac{2\pi r}{2} = \pi r \]

### Step 3: Calculate the Diameter
The diameter \( d \) of a circle is twice the radius:
\[ d = 2r \]

### Step 4: Calculate the Total Perimeter
The total perimeter \( P \) of the semi-circle is the sum of the curved length and the diameter:
\[ P = \text{Curved Length} + \text{Diameter} = \pi r + 2r \]

### Step 5: Simplify the Expression
We can factor out \( r \) from the expression:
\[ P = r(\pi + 2) \]

### Final Answer
Thus, the perimeter of the semi-circle with radius \( r \) is:
\[ P = r(\pi + 2) \]

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