A semicircular disc has a radius of 21 cm. Find its perimeter.

Answer

To find the perimeter of a semicircular disc with a radius of 21 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information:**
- Radius (r) = 21 cm

2. **Calculate the diameter (D) of the semicircle:**
- The formula for diameter is:
\[ D = 2 \times r \]
- Substituting the value of the radius:
\[ D = 2 \times 21 = 42 \text{ cm} \]

3. **Calculate the curved part of the semicircle:**
- The formula for the circumference (perimeter) of a full circle is:
\[ P = 2 \pi r \]
- For a semicircle, the curved part is half of the circumference:
\[ \text{Curved part} = \frac{1}{2} \times 2 \pi r = \pi r \]
- Substituting the radius:
\[ \text{Curved part} = \pi \times 21 \]

4. **Calculate the total perimeter of the semicircular disc:**
- The total perimeter includes the curved part and the diameter:
\[ \text{Total Perimeter} = \text{Curved part} + D \]
- Substituting the values:
\[ \text{Total Perimeter} = \pi \times 21 + 42 \]
- Using \(\pi \approx \frac{22}{7}\):
\[ \text{Total Perimeter} = \frac{22}{7} \times 21 + 42 \]

5. **Simplify the expression:**
- Calculate \(\frac{22}{7} \times 21\):
\[ \frac{22 \times 21}{7} = \frac{462}{7} = 66 \text{ cm} \]
- Now add the diameter:
\[ \text{Total Perimeter} = 66 + 42 = 108 \text{ cm} \]

### Final Answer:
The perimeter of the semicircular disc is **108 cm**.

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