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$6.93centimeters$.

Step-by-step solution

Step 1. Given information

$\theta =\frac{1}{4}radian,A=6squarecentimeters,r=?$

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,

$\theta =\frac{1}{4}radianandA=6squarecentimeters$

Now,

The Area $A$of the sector is

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

$\Rightarrow 6=\frac{1}{2}\times r^2\times \frac{1}{4}$

$\Rightarrow 6=\frac{1}{8}{r}^2$

$\Rightarrow r^2=48$

$$\begin{gathered} \Rightarrow r=\sqrt{48} \\ \Rightarrow r\approx 6.93centimeters \end{gathered}$$