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 a sector is$1.04squareinches.$

Step-by-step solution

Step 1. Given information

$r=2inches,\theta =30°,A=?$

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,

$r=2inchesand\theta =30°=0.52radian$

Now,

The Area $A$of a sector is

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

$\Rightarrow A=\frac{1}{2}\times 2^2\times 0.52$

$\Rightarrow A=1.04squareinches$