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?

Respuesta :

3085 
[(1200xpí)/2]+1200

Answer:

The answer is [tex](600\pi+1,200)\ ft[/tex] or [tex]3,085\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

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

[tex]\frac{\pi D}{2}+D[/tex]

we have

[tex]D=1,200\ ft[/tex]

substitute the value

[tex]\frac{\pi (1,200)}{2}+1,200=(600\pi+1,200)\ ft[/tex]

[tex](600\pi+1,200)\ ft=3,085\ ft[/tex]