Question

The radius of a circle is 1 inch. What is the length of a 30° arc?

Answer 1

To find the length of a 30° arc on a circle with a radius of 1 inch, you can use the formula for the length of an arc:

\[
\text{Arc Length} = \frac{\theta}{360°} \times 2\pi r
\]

where:
- \(\theta\) is the angle in degrees,
- \(r\) is the radius of the circle.

Here, \(\theta = 30°\) and \(r = 1\) inch.

Substituting the values into the formula:

\[
\text{Arc Length} = \frac{30}{360} \times 2\pi \times 1
\]

Calculating the fraction:

\[
\frac{30}{360} = \frac{1}{12}
\]

Now plug this back into the equation:

\[
\text{Arc Length} = \frac{1}{12} \times 2\pi \times 1 = \frac{2\pi}{12} = \frac{\pi}{6}
\]

Thus, the length of the 30° arc is:

\[
\frac{\pi}{6} \text{ inches}
\]

If you need a numerical approximation:

\[
\frac{\pi}{6} \approx 0.5236 \text{ inches}
\]

So the length of the 30° arc is \(\frac{\pi}{6}\) inches, or approximately 0.524 inches.