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 area of sector is$9.41squaremeters$.

Step-by-step solution

Step 1. Given information

$r=3meters,\theta =120°,A=?$

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,

$r=3metersand\theta =120°=2.09radian$

Now,

The area $A$of a sector is

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

$A=\frac{1}{2}\times 3^2\times 2.09$

$A\approx 9.41squaremeters$