Q. 80 - Precalculus Enhanced with Graphing Utilities

Question

In the problem, $A$ denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places 

Step-by-Step Solution

Answer

The required Area of sector is $36 squarefeet.$

Step 1. Given information

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

Step 2. Formula Used

The area $A$ of the sector of a circle of radius $r$ formed by the central angle of  $\theta$ radians is

$A=\frac{1}{2}{r}^2\theta$

Step 3. Calculation

We have,

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

Now,

The area $A$ of a sector is

$A=\frac{1}{2}{r}^2\theta$

$\Rightarrow A=\frac{1}{2}\times 6^2\times 2$

$\Rightarrow A=36 squarefeet$