so.. if hmm check the picture below, the radius is half that diameter
thus [tex]\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\qquad
\begin{cases}
h=height\\
r=radius=\frac{diameter}{2}\\
----------\\
h=2\frac{1}{2}\to \cfrac{5}{2}\\
diameter=1\frac{1}{2}\to \cfrac{3}{2}\\
r=\cfrac{\frac{3}{2}}{2}\to \cfrac{3}{4}
\end{cases}\implies V=\pi \left( \cfrac{3}{4} \right)^2\cfrac{5}{2}
\\\\\\
V=\pi \cdot \cfrac{9}{16}\cdot \cfrac{5}{2}\impliedby \textit{how much is }\frac{3}{4}\textit{ of that?}
\\\\\\
\cfrac{3}{4}\left( \pi \cdot \cfrac{9}{16}\cdot \cfrac{5}{2} \right)[/tex]
simplify that away
now.. that's how much is in the cooler in cubic feet though, not in gallons
notice, our units were in feet, thus our volume is also in feet, just cubics
so. to know how many gallons, simply divide that by 231
[tex]\bf \cfrac{\frac{3}{4}\left( \pi \cdot \frac{9}{16}\cdot \frac{5}{2} \right)}{231}\quad gallons[/tex]
