We have a path which has an area that is the difference between the outer circle (r = 18 ft) and the inner circle (r = 15 ft), showed as the shaded area.
Then, we can express the area of the path (A) as:
[tex]\begin{gathered} A=A_o-A_i \\ A=\pi r^2_o-\pi r^2_i \\ A=\pi(r^2_o-r^2_i) \\ A\approx3.14(18^2-15^2) \\ A\approx3.14(324-225) \\ A\approx3.14\cdot99 \\ A\approx310.86\text{ yd}^{2} \end{gathered}[/tex]Ao: area of the outer circle
Ai: area of the inner circle
ro: radius of the outer circle
ri: radius of the inner circle
As the path has an area of 310.86 square yard and a bag of sand covers 8 square yard per bag, we can calculate the number of bags (n) dividing the path area by the area covered by one bag:
[tex]n=\frac{A}{b}=\frac{310.86yd^2}{\frac{9yd^2}{\text{bag}}}=34.54\text{ bags}\approx35\text{ bags}[/tex]Answer: 35 bags of sand are needed.
