Question
page 14 of 14 Radian Angle Measure Quick Check 4 of 54 of 5 Items Question If the radius of a circle is 10 feet and the central angle is 3π4 , then what is the arc length in radians?(1 point) Responses 15π2 Start Fraction 15 pi over 2 End Fraction 15π 15 pi 30π 30 pi 60π 60 pi Skip to navigation
Answers
GPT-4o mini
To find the arc length of a circle given the radius and the central angle in radians, you can use the formula:
\[
\text{Arc Length} = r \cdot \theta
\]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Given:
- The radius \( r = 10 \) feet
- The central angle \( \theta = \frac{3\pi}{4} \)
Now plug in the values:
\[
\text{Arc Length} = 10 \cdot \frac{3\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2}
\]
Therefore, the arc length is:
\[
\frac{15\pi}{2}
\]
From the given options, the correct response is:
**15π/2**
\[
\text{Arc Length} = r \cdot \theta
\]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Given:
- The radius \( r = 10 \) feet
- The central angle \( \theta = \frac{3\pi}{4} \)
Now plug in the values:
\[
\text{Arc Length} = 10 \cdot \frac{3\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2}
\]
Therefore, the arc length is:
\[
\frac{15\pi}{2}
\]
From the given options, the correct response is:
**15π/2**