What is the arc length of a circle with diameter 8 cm and angle 180°?

The arc length of a circle with diameter 8 cm and angle 180° is 12.57 cm.

To find the arc length of a circle, you need to know the radius and the angle in degrees. The formula for the arc length \( L \) is given by:

\[ L = \frac{\theta}{360} \times 2\pi r \]

where \( \theta \) is the angle in degrees and \( r \) is the radius of the circle. In this case, the diameter of the circle is 8 cm, so the radius \( r \) is half of that, which is 4 cm.

Given that the angle \( \theta \) is 180°, we can substitute these values into the formula:

\[ L = \frac{180}{360} \times 2\pi \times 4 \]

Simplify the fraction \(\frac{180}{360}\) to \(\frac{1}{2}\):

\[ L = \frac{1}{2} \times 2\pi \times 4 \]

Next, multiply the constants:

\[ L = \pi \times 4 \]

Since \(\pi\) (pi) is approximately 3.14, we can calculate:

\[ L = 3.14 \times 4 = 12.56 \]

Rounding to two decimal places, the arc length is approximately 12.57 cm. This means that the length of the curved part of the circle corresponding to a 180° angle is 12.57 cm. This is half the circumference of the circle, as 180° represents half of the full 360° circle.