find the area of the smaller sector.\nround 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})