Q. 72 - 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.

$r=6$ feet,      $\theta =2$ radians,      $s=?$

Step-by-Step Solution

Answer

The length $s$ of the arc is $12 feet.$

Step 1. Given information

$r=6 feet , \theta =2 radians , s=?$

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,

$r=6 feet and \theta =2 radians$

The length $s$ of the arc is

$s=r\theta$

$\Rightarrow s=6\times 2$

$\Rightarrow s=12$ feet