We have that the circumference of a circle can be represented with the following equation:
![C=\pi d](https://img.qammunity.org/2023/formulas/mathematics/high-school/4mkash3xbv1k0yoiexwvsolvp2d8x0dvan.png)
where d represents the diameter of the circle.
In this case, we have a circle of circumference C = 30 ft made with the lights, then, using the equation and solving for d, assuming that pi equals 3.14, we get:
![\begin{gathered} 30=(3.14)d \\ \Rightarrow d=(30)/(3.14)=9.55\approx10ft \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bdec512tcqq8rlxrxgvi7377r8b22lq1dy.png)
therefore, the approximate diameter of the largest circle is 10 ft