Question

find the area of the sector of a circle of radius 10 m with a central angle of $\frac{5pi}{7}$. 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: Substitute given values

We are given that $r = 10$ m and $\theta=\frac{5\pi}{7}$. Substitute these values into the formula:
$A=\frac{1}{2}(10)^{2}\times\frac{5\pi}{7}$
$A=\frac{1}{2}\times100\times\frac{5\pi}{7}$
$A = 50\times\frac{5\pi}{7}$
$A=\frac{250\pi}{7}$

Step3: Calculate the numerical value

$A=\frac{250\pi}{7}\approx\frac{250\times3.14159}{7}$
$A\approx\frac{785.3975}{7}\approx112.20$

Answer:

$112.20$ m²