Question
Find the length of the arc for a circle with a radius of 18 inches and a central angle of 300°. (1 point) Responses 270π inches 270π inches 8π3 inches 8π3 inches 30π inches 30π inches 324π inches
Answers
GPT-4o mini
To find the length of the arc for a circle, we can use the formula:
\[
L = r \theta
\]
where \( L \) is the length of the arc, \( r \) is the radius, and \( \theta \) is the central angle in radians.
First, we need to convert the angle from degrees to radians. The conversion is done using the relationship:
\[
\text{Radians} = \text{Degrees} \times \left(\frac{\pi}{180}\right)
\]
For a central angle of \( 300^\circ \):
\[
\theta = 300 \times \left(\frac{\pi}{180}\right) = \frac{300\pi}{180} = \frac{5\pi}{3} \, \text{radians}
\]
Now, we can calculate the length of the arc using the radius \( r = 18 \) inches:
\[
L = r \theta = 18 \times \frac{5\pi}{3} = 18 \times \frac{5\pi}{3} = 30\pi \, \text{inches}
\]
Thus, the length of the arc is:
\[
\boxed{30\pi} \, \text{inches}
\]
\[
L = r \theta
\]
where \( L \) is the length of the arc, \( r \) is the radius, and \( \theta \) is the central angle in radians.
First, we need to convert the angle from degrees to radians. The conversion is done using the relationship:
\[
\text{Radians} = \text{Degrees} \times \left(\frac{\pi}{180}\right)
\]
For a central angle of \( 300^\circ \):
\[
\theta = 300 \times \left(\frac{\pi}{180}\right) = \frac{300\pi}{180} = \frac{5\pi}{3} \, \text{radians}
\]
Now, we can calculate the length of the arc using the radius \( r = 18 \) inches:
\[
L = r \theta = 18 \times \frac{5\pi}{3} = 18 \times \frac{5\pi}{3} = 30\pi \, \text{inches}
\]
Thus, the length of the arc is:
\[
\boxed{30\pi} \, \text{inches}
\]