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.

Short answer

The required radius of the circle is $3.46$feet.

Step-by-step solution

Step 1. Given information

$\theta =\frac{1}{3}radians,A=2squarefeet,r=?$

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,

$\theta =\frac{1}{3}radians,A=2squarefeet$

Now,

The area $A$of a sector is

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

role="math" localid="1647078850622" $\Rightarrow 2=\frac{1}{2}\times r^2\times \frac{1}{3}$

role="math" localid="1647078839980" $$\begin{gathered} \Rightarrow 2=\frac{1}{6}{r}^2 \\ \Rightarrow r^2=12 \\ \Rightarrow r=\sqrt{12} \\ \Rightarrow r\approx 3.46feet \end{gathered}$$