If the perimeter of a semi-circle is 36 cm, then find its radius (in cm).

Options

A. 7
B. 14
C. 13
D. 26

Answer

To find the radius of a semicircle given its perimeter, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the perimeter of a semicircle**:
The perimeter (P) of a semicircle can be expressed as:
\[ P = \pi r + 2r \]
where \( r \) is the radius of the semicircle.

2. **Set up the equation**:
According to the problem, the perimeter of the semicircle is given as 36 cm. Therefore, we can set up the equation:
\[ \pi r + 2r = 36 \]

3. **Factor out the radius**:
We can factor out \( r \) from the left side of the equation:
\[ r(\pi + 2) = 36 \]

4. **Solve for the radius \( r \)**:
To isolate \( r \), divide both sides of the equation by \( (\pi + 2) \):
\[ r = \frac{36}{\pi + 2} \]

5. **Substitute the value of \( \pi \)**:
Using \( \pi \approx 3.14 \):
\[ r = \frac{36}{3.14 + 2} = \frac{36}{5.14} \]

6. **Calculate the value of \( r \)**:
Now, perform the division:
\[ r \approx \frac{36}{5.14} \approx 7.0 \text{ cm} \]

### Final Answer:
The radius of the semicircle is approximately \( 7 \) cm.

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