Q. 86 - 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 sector is $9.41 square meters$.

Step 1. Given information

$r=3 meters , \theta =120° , A=?$

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,

$r=3 meters and \theta =120°=2.09 radian$

Now, 

The area $A$ of a sector is

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

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

$A\approx 9.41 square meters$