A contractor has installed a silt fence around an area that is semi-circular and level to prevent soil from the construction site entering nearby streams. The diameter of the semi-circle is 1200 feet. How many linear feet of fence does the contractor need to use to enclose the area?
Answer:
The answer is \((600\pi+1,200)\ ft\) or \(3,085\ ft\)
Step-by-step explanation:
we know that
The circumference of a circle is equal to
\(C=\pi D\)
where
D is the diameter of the circle
In this problem, to calculate how many linear feet are needed, find the perimeter of a semicircle
so
\(\frac{\pi D}{2}+D\)
we have
\(D=1,200\ ft\)
substitute the value
\(\frac{\pi (1,200)}{2}+1,200=(600\pi+1,200)\ ft\)
\((600\pi+1,200)\ ft=3,085\ ft\)