Question

A right circular cylinder has a height of ​19 3/4​ ft and a diameter ​1 2/5​ times its height. What is the volume of the cylinder? Enter your answer as a decimal in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answer 1

let's first off convert the mixed fractions to improper fractions, and then get its volume, bearing in mind that the radius is half the diameter.

$\stackrel{mixed}{19\frac{3}{4}}\implies \cfrac{19\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{79}{4}} ~\hfill \stackrel{mixed}{1\frac{2}{5}}\implies \cfrac{1\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{7}{5}} \\\\[-0.35em] ~\dotfill$

$\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=\frac{79}{4}\\[1em] r=\frac{7}{5}\cdot \frac{1}{2}\\ \qquad \frac{7}{10} \end{cases}\implies \begin{array}{llll} V=\pi \left( \cfrac{7}{10} \right)^2\left( \cfrac{79}{4} \right)\\\\ V=(3.14) \left( \cfrac{7}{10} \right)^2\left( \cfrac{79}{4} \right)\\\\ V\approx 30.39 \end{array}$