Q. 79 - 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 $25 mete{r}^2$.

Step 1. Given information

$r=10 meters, \theta =\frac{1}{2} radian, A=?$

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,

$r=10 meters, \theta =\frac{1}{2} radian$

Now, 

The area A of a sector is

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

$\Rightarrow A=\frac{1}{2}\times {10}^2\times \frac{1}{2}$

$\Rightarrow A=25 metersquare$