Question

find the area of the smaller sector.
area = ?m²
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 and \(r\) is the radius of the circle.

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

From the problem, \(\theta = 40^{\circ}\) and \(r = 8\space m\).

Step3: Substitute the values into the formula

Substitute \(\theta = 40\) and \(r = 8\) into \(A=\frac{\theta}{360}\times\pi r^{2}\).

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Step4: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(A=\frac{64\times3.14159}{9}\approx22.34\space m^{2}\)

Answer:

\(22.34\space m^{2}\)