Question

The diameter of a circle is 6 centimeters. What is the length of a 60° arc?

Answer 1

To find the length of a 60° arc in a circle with a diameter of 6 centimeters, we can follow these steps:

1. **Calculate the radius**: The radius \( r \) is half of the diameter.
\[
r = \frac{diameter}{2} = \frac{6 \, cm}{2} = 3 \, cm
\]

2. **Calculate the circumference of the circle**: The circumference \( C \) of a circle is given by the formula
\[
C = 2 \pi r
\]
Substituting in the radius we found:
\[
C = 2 \pi (3 \, cm) = 6 \pi \, cm
\]

3. **Find the length of the arc**: The length of an arc is a fraction of the circumference, depending on the angle in degrees. The formula to find the length \( L \) of an arc is:
\[
L = \frac{\theta}{360^\circ} \times C
\]
where \( \theta \) is the angle in degrees. For a 60° arc:
\[
L = \frac{60^\circ}{360^\circ} \times 6 \pi \, cm
\]

4. **Calculate the arc length**:
\[
L = \frac{1}{6} \times 6 \pi \, cm = \pi \, cm
\]

Thus, the length of the 60° arc is:
\[
\boxed{\pi \, cm}
\]