Question

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 1100 feet. How many linear feet of fence does the contractor need to use to enclose the area?
How many acres are within the enclosed by the fence?

Answer 1

We know is a semi-circle, so let us use the equation for the area of a circle instead, and then, half it
so, the diameter is 1100, meaning the radius is half that, or 550

so...$\textit{area of a circle}=\pi r^2\qquad r=radius=\frac{diameter}{2}=\frac{1100}{2}=550 \\ \quad \\ \textit{area of a semi-circle}=\cfrac{\pi r^2}{2}\impliedby \textit{enclosed acres} \\ \quad \\ \textit{circumference of a circle}=2\pi r \\ \quad \\ \textit{circumference of a semi-circle}=\cfrac{2\pi r}{2}\impliedby \textit{linear feet of fence}$