Respuesta :
let's firstly convert the mixed fractions to improper fractions.
[tex]\bf \stackrel{mixed}{22\frac{1}{4}}\implies \cfrac{22\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{89}{4}}~\hfill \stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{the diameter is }\frac{12}{5}\textit{ of }\frac{89}{4}}{\cfrac{89}{4}\cdot \cfrac{12}{5}}\implies \cfrac{267}{5}\implies \stackrel{\textit{the radius is }\frac{1}{2}\textit{ of the diameter}}{\cfrac{267}{5}\cdot \cfrac{1}{2}}\implies \stackrel{radius}{\cfrac{267}{10}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=\frac{267}{10}\\[1em] h=\frac{89}{4} \end{cases}\implies V=\pi \left( \frac{267}{10} \right)^2\left( \frac{89}{4} \right) \\\\\\ V=\pi (15861.8025)\implies \stackrel{\pi =3.14}{V=49806.05985}\implies V=\stackrel{\textit{rounded up}}{49806.06}[/tex]
