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 of $\theta$ and $r$

The radius $r = 6$ inches and the central - angle of the smaller sector $\theta=360^{\circ}-140^{\circ}=220^{\circ}$.

Step3: Substitute values into the formula

$A=\frac{220^{\circ}}{360^{\circ}}\times\pi\times(6)^{2}$. First, calculate $(6)^{2}=36$. Then, $\frac{220}{360}\times36\pi$. $\frac{220}{360}\times36 = 22$. So, $A = 22\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14159$, we have $A\approx22\times3.14159 = 69.11498\approx69.11$ square inches.

Answer:

$69.11$