find the area of the smaller sector. area = ?m² round your answer to the nearest hundredth.

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector in degrees and $r$ is the radius of the circle.

Step2: Identify values of $\theta$ and $r$

Given that $r = 8$ m and $\theta=40^{\circ}$.

Step3: Substitute values into the formula

$A=\frac{40^{\circ}}{360^{\circ}}\times\pi\times(8)^{2}$. First, simplify $\frac{40}{360}=\frac{1}{9}$. Then, $(8)^{2}=64$. So, $A=\frac{1}{9}\times\pi\times64=\frac{64\pi}{9}$.

Step4: Calculate the value and round

$A=\frac{64\pi}{9}\approx\frac{64\times3.14159}{9}=\frac{201.06176}{9}\approx22.34$ $m^{2}$.

Answer:

$22.34$ $m^{2}$