Step 1
The circular hot tube is in the shape of a cylinder. Therefore its volume will be;
[tex]v=\pi\times r^2\times h[/tex]where;
[tex]\begin{gathered} circumference=2\times\pi\times r=25.12ft \\ h=3.5feet \end{gathered}[/tex]Find r, using the circumference
[tex]\begin{gathered} 2\times\pi\times r=25.12 \\ \pi r=\frac{25.12}{2} \\ r=\frac{25.12}{2\pi} \\ \end{gathered}[/tex]Step 2
Find the volume of the hot tube at 100%
[tex]\begin{gathered} v=\pi\times(\frac{25.12}{2\pi})^2\times3.5 \\ v=3.5\pi\frac{25.12^2}{2^2\pi^2} \\ v=3.5\times\:50.21453046 \\ v=175.7508566ft^3 \end{gathered}[/tex]Step 3
Find the recommended capacity which is 80% full
[tex]\begin{gathered} \frac{175.7508566}{x}=\frac{100}{80} \\ x=140.6006853ft^3 \\ \end{gathered}[/tex]Note; 1 Cubic foot=7.48052 gallons of water. Therefore, the water Rita should put in the hot tub will be;
[tex]\begin{gathered} \frac{140.6006853ft^3}{1ft^3}=\frac{y}{7.48052} \\ y=1051.766238\text{ gallons of water} \\ \approx1051.77\text{ gallons of water} \end{gathered}[/tex]Answer;
[tex]1051.77\text{ gallons of water}[/tex]