Question

Consider circle C with angle ACB measuring 3
radians.
If minor arc AB measures 9n inches, what is the length of
the radius of circle C? If necessary, round your answer to
the nearest inch.
6 inches
12 inches
18 inches
24 inches

Answer 1

Answer:

Radius of circle C= 3in

Step-by-step explanation:

We are given that a circle C .

Measure of an angle ACB=$\theta=3$ radians

Measure of minor arc=$9$ in

We have to find the radius of circle C.

We know that

$\theta=\frac{l}{r}$

Where $\theta$ in radians

Substitute the value in the given formula

$3=\frac{9}{r}$

$r=\frac{9}{3}=3 in$

Hence, the radius of circle C=3 in

But, options do not match with this answer.

Answer 2

Since the minor arc (AB) measures 9π inches, the length of the radius of this circle is equal to: B. 12 inches.

Given the following data:

• Central angle = 3π/4 radians.

• Arc length = 9π inches.

How to calculate the radius of the circle?

In Mathematics, if you want to calculate the radius of a circle with a minor arc, you should divide the central angle (in degrees) that is subtended by the arc by 360 degrees and then multiply it by the circumference of the circle.

Conversion:

3π/4 radians to degrees = (3 × 180)/4 = 135 degrees.

Mathematically, the arc length formed by a circle is given by:

Arc length = 2πr × θ/360

9π = 2πr × 135/360

9 = 2r × 0.375

0.75r = 9

r = 9/0.75

Radius, r = 12 inches.

Read more on radius here: brainly.com/question/14478195