Question

Question
If a circle has a circumference of 20π
and a central angle of 90 degrees is drawn, then what is the length of the minor arc?(1 point)

Answer 1

To find the length of the minor arc in a circle with a given circumference and central angle, we can use the formula for the length of an arc:

\[
\text{Arc Length} = \left(\frac{\theta}{360}\right) \times C
\]

where:
- \( \theta \) is the central angle in degrees,
- \( C \) is the circumference of the circle.

Given that the circumference \( C = 20\pi \) and the central angle \( \theta = 90^\circ \), we can substitute these values into the formula:

\[
\text{Arc Length} = \left(\frac{90}{360}\right) \times 20\pi
\]

Simplifying the fraction:

\[
\frac{90}{360} = \frac{1}{4}
\]

Now substituting this back into the equation:

\[
\text{Arc Length} = \frac{1}{4} \times 20\pi = 5\pi
\]

Thus, the length of the minor arc is \( 5\pi \).