Question

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

Explanation:

Step1: Write the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Here, \(\theta = 80^{\circ}\) and \(r = 8\space m\). So, \(A=\frac{80}{360}\times\pi\times(8)^{2}\).
First, calculate \(\frac{80}{360}=\frac{2}{9}\), and \((8)^{2}=64\). Then \(A=\frac{2}{9}\times\pi\times64\).

Step3: Calculate the value

\(A=\frac{128\pi}{9}\approx\frac{128\times3.14159}{9}\).
\(128\times3.14159 = 402.12352\). Then \(\frac{402.12352}{9}\approx44.68\space m^{2}\).

Answer:

\(44.68\space m^{2}\)