Find the perimeter of a semicircle of radius 7 cm.

Explanation

To find the perimeter of a semicircle with a radius of 7 cm, we can follow these steps:

### Step 1: Understand the components of the semicircle
A semicircle consists of two parts: the curved part (which is half of the circumference of a full circle) and the straight part (which is the diameter).

### Step 2: Calculate the diameter
The diameter (d) of a circle is twice the radius (r).
- Formula: \( d = 2r \)
- Given: \( r = 7 \, \text{cm} \)
- Calculation:
\[ d = 2 \times 7 = 14 \, \text{cm} \]

### Step 3: Calculate the circumference of the full circle
The circumference (C) of a full circle is given by the formula:
- Formula: \( C = 2\pi r \)
- Given: \( r = 7 \, \text{cm} \)
- Calculation:
\[ C = 2 \times \pi \times 7 = 14\pi \, \text{cm} \]

### Step 4: Calculate the length of the curved part of the semicircle
Since we only need the curved part of the semicircle, we take half of the circumference:
- Calculation:
\[ \text{Curved length} = \frac{C}{2} = \frac{14\pi}{2} = 7\pi \, \text{cm} \]

### Step 5: Calculate the perimeter of the semicircle
The perimeter (P) of the semicircle is the sum of the curved length and the diameter:
- Formula: \( P = \text{Curved length} + \text{Diameter} \)
- Calculation:
\[ P = 7\pi + 14 \, \text{cm} \]

### Step 6: Substitute the value of \(\pi\) (approximately 3.14) to find the numerical value
- Calculation:
\[ P \approx 7 \times 3.14 + 14 \approx 21.98 + 14 \approx 35.98 \, \text{cm} \]

Thus, the perimeter of the semicircle is approximately **36 cm**.

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