Q. 74 - Precalculus Enhanced with Graphing Utilities

Question

In the problem, $s$ denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$\theta =\frac{1}{4}$radian,        $s=6$ centimeters,        $r=?$

Step-by-Step Solution

Answer

The radius of the circle is $24$centimeters.

Step 1. Given information

$\theta =\frac{1}{4}radian , s=6 centimeters , r=?$$\theta =\frac{1}{4} radian, s=6 centimeters, r=?$

Step 2. Formula Used

For a circle of radius $r$ , a central angle of $\theta$  radians subtends an arc whose length $s$ is

                      $s=r\theta$

Step 3. Calculation

We have, 

$\theta =\frac{1}{4}radian and s=6centimeters$

Now,

The length s of the arc is

$$\begin{gathered} s=r\theta \\ \Rightarrow r=\frac{s}{\theta } \end{gathered}$$

$\Rightarrow r=\frac{6}{{\displaystyle \frac{1}{4}}}$

$\Rightarrow r=24centimeters$