Consider circle C with angle ACB measuring 3 pi/4 radians if minor arc AB measures 9 pi inches what is the length of the radius of circle C if necessary round your answer to the nearest inch

r = 12 inches

Step-by-step explanation:

In this question, we are asked to calculate the length of the radius of the circle.

This is accessible from using the length of an arc.

Mathematically, the length of an arc can be calculated using the formula;

Theta/360 * 2 * pi * r

Where Theta is the angle subtended at the center and r is the radius of he circle.

According to the question, Theta is 3pi/4 radians or let's just say 0.75pi. This to degrees will be 135 degrees (pi = 180 degrees)

Thus we have;

9 pi = 135/360 * 2 * pi * r

divide through by pi

9 = 270r/360

360 * 9 = 270r

r = (360 * 9) / 270

r = 12 inches