If the perimeter of a semi-circular protractor is 36cm, then its diameter is?

Options

A. a. 6cm
B. b. 7cm
C. c. 7.5cm
D. d. 14cm

Answer

To find the diameter of a semicircular protractor given its perimeter, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Perimeter of a Semicircle**:
The perimeter (or circumference) of a semicircular protractor consists of the curved part (which is half the circumference of a full circle) and the straight part (the diameter).

The formula for the perimeter \( P \) of a semicircle is:
\[ P = \pi r + 2r \]
where \( r \) is the radius of the semicircle.

2. **Set Up the Equation**:
We know from the problem that the perimeter is given as 36 cm. Thus, we can set up the equation:
\[ \pi r + 2r = 36 \]

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

4. **Substitute the Value of \( \pi \)**:
Using \( \pi \approx \frac{22}{7} \), we substitute this value into the equation:
\[ r\left(\frac{22}{7} + 2\right) = 36 \]

5. **Convert 2 to a Fraction**:
To add \( \frac{22}{7} \) and 2, we convert 2 into a fraction:
\[ 2 = \frac{14}{7} \]
So, we have:
\[ r\left(\frac{22}{7} + \frac{14}{7}\right) = 36 \]
This simplifies to:
\[ r\left(\frac{36}{7}\right) = 36 \]

6. **Solve for \( r \)**:
To isolate \( r \), multiply both sides by the reciprocal of \( \frac{36}{7} \):
\[ r = 36 \times \frac{7}{36} \]
Simplifying this gives:
\[ r = 7 \text{ cm} \]

7. **Calculate the Diameter**:
The diameter \( d \) is twice the radius:
\[ d = 2r = 2 \times 7 = 14 \text{ cm} \]

### Final Answer:
The diameter of the semicircular protractor is **14 cm**.

---