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 central angle$\theta$is$0.44radian$

Step-by-step solution

Step 1. Given information

$r=6meters,A=8squaremeters,\theta =?$

Step 2. Formula Used 

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

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

Step 3. Calculation

We have,

$r=6metersandA=8squaremeters$

Now,

The Area $A$of a sector is

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

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

$\Rightarrow 8=\frac{36}{2}\times \theta$

$\Rightarrow \theta =0.44radian$