Question

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

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Identify the values of \(\theta\) and \(r\)

From the problem, \(\theta = 140^{\circ}\) and \(r = 6\) inches.

Step3: Substitute the values into the formula

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Step4: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(A = 14\times3.14159\approx43.98\)

Answer:

\(43.98\)