The volume of a cylinder is given by:
![V=h\pi r^2](https://img.qammunity.org/2023/formulas/mathematics/college/lw6lf7nyx8az67dbrljior9uvb34i29hnd.png)
where h is the height and r is the radius. In this case the height is 4.5 ft and since the diameter is 16 ft, this means that the radius is 8 ft. Plugging this values into the equation above we have:
![\begin{gathered} V=(4.5)(\pi)(8) \\ V=36\pi \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/o6d58r6gxhur1pk7ruigoxr6s1gjapnsma.png)
Therefore the capacity of the swiming pool is:
![36\pi](https://img.qammunity.org/2023/formulas/mathematics/college/pcvjrc10jp2072jvvyj1bouyru43bened3.png)
cubic feet.