Question

find the area of the sector of a circle of radius 18 m with a central angle of $\frac{12pi}{7}$. round the solution to two decimal places.

Explanation:

Step1: Recall 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: Identify the values of $r$ and $\theta$

Given that $r = 18$ m and $\theta=\frac{12\pi}{7}$.

Step3: Substitute the values into the formula

$A=\frac{1}{2}(18)^{2}\times\frac{12\pi}{7}$.
First, calculate $(18)^{2}=324$. Then, $A=\frac{1}{2}\times324\times\frac{12\pi}{7}$.
$\frac{1}{2}\times324 = 162$. So, $A = 162\times\frac{12\pi}{7}=\frac{1944\pi}{7}$.

Step4: Calculate the numerical value

$A=\frac{1944\pi}{7}\approx\frac{1944\times3.14159}{7}$.
$1944\times3.14159 = 6107.25096$.
$A=\frac{6107.25096}{7}\approx872.46$.

Answer:

$872.46$ m²