Question

A right circular cylinder has a height of 22 1/4 ft and a diameter 2 2/5 times its height.



What is the volume of the cylinder?

Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answer 1

let's firstly convert the mixed fractions to improper fractions.

$\bf \stackrel{mixed}{22\frac{1}{4}}\implies \cfrac{22\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{89}{4}}~\hfill \stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{the diameter is }\frac{12}{5}\textit{ of }\frac{89}{4}}{\cfrac{89}{4}\cdot \cfrac{12}{5}}\implies \cfrac{267}{5}\implies \stackrel{\textit{the radius is }\frac{1}{2}\textit{ of the diameter}}{\cfrac{267}{5}\cdot \cfrac{1}{2}}\implies \stackrel{radius}{\cfrac{267}{10}} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=\frac{267}{10}\\[1em] h=\frac{89}{4} \end{cases}\implies V=\pi \left( \frac{267}{10} \right)^2\left( \frac{89}{4} \right) \\\\\\ V=\pi (15861.8025)\implies \stackrel{\pi =3.14}{V=49806.05985}\implies V=\stackrel{\textit{rounded up}}{49806.06}$