Question

find the area of the smaller sector. 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 and $r$ is the radius of the circle.

Step2: Identify values

The radius $r = 8$ m and the central - angle of the smaller sector $\theta=360^{\circ}-140^{\circ}=220^{\circ}$.

Step3: Substitute values into formula

$A=\frac{220^{\circ}}{360^{\circ}}\times\pi\times(8)^{2}=\frac{220}{360}\times\pi\times64=\frac{22}{36}\times64\pi=\frac{22\times64\pi}{36}=\frac{1408\pi}{36}=\frac{352\pi}{9}\approx122.72$ m².

Answer:

$122.72$ m²