Question

Consider circle c with angle 3/4 radians. If minor arc AB measures 9n inches, what is the length of

Answer 1

The radius of circle is 12 inches

Solution:

Given that,

Consider circle c with angle $\frac{3 \pi }{4} \text{ radians }$

Minor arc AB measures $9 \pi$ inches

Therefore, we can say,

$Central\ angle\ in\ radians = \frac{3 \pi }{4}\\\\Arc\ length = 9 \pi$

To find: Radius of circle

The length of arc when angle given in radians is:

$s = r \times \theta$

Where,

"s" is the arc length and "r" is the radius and $\theta$ is the central angle in radians

$9 \pi = r \times \frac{3 \pi }{4}\\\\r = 9 \times \frac{4}{3}\\\\r = 12$

Thus the radius of circle is 12 inches