Question

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?

Answer 1

`\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{(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}`

plug in your radius