The diameter of a circle is 16 centimetres. What is the length of a 180° arc?

To find the length of a 180° arc (which is a semicircle), we use the formula for the arc length:

\[
\text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi r
\]

Where:
- \(\theta = 180^\circ\) is the angle of the arc,
- \(r\) is the radius of the circle,
- \(\pi\) is approximately 3.14159.

### Step-by-step solution:
1. The diameter of the circle is 16 cm, so the radius \(r\) is half of that:
   \[
   r = \frac{16}{2} = 8 \, \text{cm}
   \]
2. Substituting the values into the formula for the arc length:
   \[
   \text{Arc length} = \frac{180}{360} \times 2\pi \times 8
   \]
3. Simplifying:
   \[
   \text{Arc length} = \frac{1}{2} \times 2\pi \times 8 = \pi \times 8
   \]
4. Finally:
   \[
   \text{Arc length} = 8\pi \, \text{cm}
   \]

Thus, the length of the 180° arc is approximately:
\[
8\pi \approx 25.13 \, \text{cm}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the arc length change for a 90° arc of the same circle?
2. What would be the circumference of the entire circle?
3. How do we find the area of the same circle?
4. How would the arc length change if the diameter was doubled?
5. How do we calculate the length of any arc for a given angle?

**Tip:** For any circular measurement, always remember to distinguish between radius and diameter!

Learn how to find the length of a 180° arc in a circle with a diameter of 16 cm. This solution covers important concepts such as the arc length formula and calculating radius from the diameter. Suitable for Grades 6-8 students.

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