A designer wants to make use of a half-spherical cistern in a water system. If the cistern has a diameter of 5.5 feet, how many gallons of water can it hold?
[tex]\textit{volume of a sphere}=\cfrac{4}{3}\pi r^3\qquad r=radius
\\ \quad \\
\textit{so, a half of that, or a half-sphere volume}=\cfrac{\frac{4}{3}\pi r^3}{2}
\\ \quad \\
\cfrac{4}{3}\pi r^3\cdot \cfrac{1}{2}\implies \cfrac{4\pi r^3}{6}\implies \cfrac{2\pi r^3}{3}[/tex]
