Chapter 4, Problem 1RE

Find the radian measure of the central angle of a circle of radius 6 centimeters that intercepts an arc of length27 centimeters.

To determine

To calculate: The radian measure of the central angle of the provided circle of radius 6 cm that intercepts an arc of length 27 cm.

Answer to Problem 1RE

Solution:

The radian measure of the central angle made by the arc is $\underset{\_}{4.5\text{ radians}}$.

Explanation of Solution

Given information:

The radius of the circle = 6 cm

Length of arc = 27 cm

Formula used:

$(\text{central angle})\theta =\frac{\text{length of arc}}{\text{radius}}$

Calculation:

We know that the measure of the angle made by the arc at the center is:

$\begin{array}{c}\theta =\frac{\text{length of arc}}{\text{radius}}\\ =\frac{27}{6}\\ =4.5\text{ radians}\end{array}$

Hence, the radian measure of the central angle made by the arc is $\underset{\_}{4.5\text{ radians}}$.