If the perimeter of a semicircle is 18 cm, what will be its diameter ?

Options

A. 9 cm
B. 28 cm
C. 14 cm
D. 7 cm

Answer

To find the diameter of a semicircle given that its perimeter is 18 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Perimeter of a Semicircle**:
The perimeter (P) of a semicircle can be expressed as:
\[ P = \frac{1}{2} \times 2\pi r + d \]
where \(d\) is the diameter and \(r\) is the radius. Since the diameter \(d\) is twice the radius (\(d = 2r\)), we can substitute \(r\) with \(\frac{d}{2}\).

2. **Substitute the Radius**:
Replacing \(r\) in the perimeter formula gives:
\[ P = \frac{1}{2} \times 2\pi \left(\frac{d}{2}\right) + d \]
Simplifying this, we have:
\[ P = \pi \left(\frac{d}{2}\right) + d \]

3. **Set Up the Equation**:
We know from the problem that the perimeter is 18 cm, so we can write:
\[ \pi \left(\frac{d}{2}\right) + d = 18 \]

4. **Substitute the Value of \(\pi\)**:
Using \(\pi \approx \frac{22}{7}\), we substitute this value into the equation:
\[ \frac{22}{7} \left(\frac{d}{2}\right) + d = 18 \]

5. **Clear the Fraction**:
To eliminate the fraction, multiply the entire equation by 7:
\[ 22 \left(\frac{d}{2}\right) + 7d = 126 \]
This simplifies to:
\[ 11d + 7d = 126 \]

6. **Combine Like Terms**:
Combine the terms involving \(d\):
\[ 18d = 126 \]

7. **Solve for \(d\)**:
Divide both sides by 18 to find \(d\):
\[ d = \frac{126}{18} = 7 \]

### Final Answer:
The diameter of the semicircle is **7 cm**.

---