Q. 85 - Precalculus Enhanced with Graphing Utilities

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 .

Step-by-Step Solution

Answer

The required area of a sector is $1.04 square inches.$

Step 1. Given information

$r=2 inches , \theta =30° , A=?$

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, 

$r=2 inches and \theta =30°=0.52 radian$

Now,

The Area $A$ of a sector is

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

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

$\Rightarrow A=1.04 square inches$