Question

please view the following video before answering this question. lecture video, section 4.1, example 06 find the area of a sprinkler system waters if its radius is 20 ft and covers an angle of 80°. round the answer to one decimal place. ft²

Explanation:

Step1: Convert angle to radians

The formula for the area of a sector is \(A=\frac{1}{2}r^{2}\theta\), where \(\theta\) is in radians.
We know that \(\theta = 80^{\circ}\times\frac{\pi}{180}=\frac{4\pi}{9}\) radians.

Step2: Calculate the area

Given \(r = 20\) ft.
Substitute \(r\) and \(\theta\) into the formula \(A=\frac{1}{2}\times(20)^{2}\times\frac{4\pi}{9}\).
First, \((20)^{2}=400\). Then \(\frac{1}{2}\times400 = 200\).
So \(A=200\times\frac{4\pi}{9}=\frac{800\pi}{9}\approx279.25268\)

Answer:

\(279.3\)