Question

find the area of the sector of a circle having radius r and central angle θ. r = 14.1 cm, θ = $\frac{pi}{19}$

Explanation:

Step1: Recall the sector - area formula

The formula for the area of a sector of a circle is $A=\frac{1}{2}r^{2}\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians.

Step2: Substitute the given values into the formula

Given $r = 14.1$ cm and $\theta=\frac{\pi}{19}$, we substitute these values into the formula:
$A=\frac{1}{2}(14.1)^{2}\times\frac{\pi}{19}$.
First, calculate $(14.1)^{2}=14.1\times14.1 = 198.81$.
Then, $A=\frac{1}{2}\times198.81\times\frac{\pi}{19}$.
$A=\frac{198.81\pi}{38}$.
Using $\pi\approx3.14159$, we have $A=\frac{198.81\times3.14159}{38}$.
$198.81\times3.14159 = 198.81\times(3 + 0.1+0.04 + 0.001+0.0005 + 0.00009)=198.81\times3+198.81\times0.1+198.81\times0.04+198.81\times0.001+198.81\times0.0005+198.81\times0.00009 = 596.43+19.881+7.9524+0.19881+0.099405+0.0178929 = 624.5795079$.
$A=\frac{624.5795079}{38}\approx16.44$ $cm^{2}$.

Answer:

$A\approx16.44$ $cm^{2}$