Solution:
Given:
A circular field with a radius of 70-foot
To find the area watered by the irrigation system, since the field is circular, we use the area of a circle.
The area of a circle is given by;
[tex]\begin{gathered} A=\pi r^2 \\ \\ \text{where} \\ r\text{ is the radius} \\ A\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} A=\pi r^2 \\ r=70ft \\ A=\pi\times70^2 \\ A=\pi\times70\times70 \\ \text{Taking }\pi=\frac{22}{7} \\ A=\frac{22}{7}\times70\times70 \\ A=15,400ft^2 \end{gathered}[/tex]Therefore, the exact area watered by the irrigation system is;
[tex]15,400ft^2[/tex]