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$36squarefeet.$

Step-by-step solution

Step 1. Given information

$r=6feet,\theta =2radians,A=?$

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,

$r=6feetand\theta =2radians$

Now,

The area $A$of a sector is

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

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

$\Rightarrow A=36squarefeet$